top

  Info

  • Utilizzare la checkbox di selezione a fianco di ciascun documento per attivare le funzionalità di stampa, invio email, download nei formati disponibili del (i) record.

  Info

  • Utilizzare questo link per rimuovere la selezione effettuata.

Biblioteca

MARC Lista (tabellare)
Brownian motion : fluctuations, dynamics, and applications / / Robert M. Mazo
Brownian motion : fluctuations, dynamics, and applications / / Robert M. Mazo
Autore Mazo Robert M
Edizione [1st ed.]
Pubbl/distr/stampa Oxford, : Clarendon Press, 2002
Descrizione fisica 1 online resource (302 p.)
Disciplina 530.42
530.475
Collana Oxford science publications
International series of monographs on physics
Soggetto topico Brownian motion processes
Markov processes
Processos de moviment brownià
Processos estocàstics
Processos de Markov
Mecànica estadística
Difusió
Polímers
Fluctuacions (Física)
Soggetto genere / forma Llibres electrònics
ISBN 9786611998790
9781281998798
1281998796
9780191565083
0191565083
9780199556441
019955644X
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Contents; 1 Historical Background; 1.1 Robert Brown; 1.2 Between Brown and Einstein; 1.3 Albert Einstein; 1.4 Marian von Smoluchowski; 1.5 Molecular Reality; 1.6 The Scope of this Book; 2 Probability Theory; 2.1 Probability; 2.2 Conditional Probability and Independence; 2.3 Random Variables and Probability Distributions; 2.4 Expectations and Particular Distributions; 2.5 Characteristic Function; Sums of Random Variables; 2.6 Conclusion; 3 Stochastic Processes; 3.1 Stochastic Processes; 3.2 Distribution Functions; 3.3 Classification of Stochastic Processes; 3.4 The Fokker-Planck Equation
3.5 Some Special Processes3.6 Calculus of Stochastic Processes; 3.7 Fourier Analysis of Random Processes; 3.8 White Noise; 3.9 Conclusion; 4 Einstein-Smoluchowski Theory; 4.1 What is Brownian Motion?; 4.2 Smoluchowski's Theory; 4.3 Smoluchowski Theory Continued; 4.4 Einstein's Theory; 4.5 Diffusion Coefficient and Friction Constant; 4.6 The Langevin Theory; 5 Stochastic Differential Equations and Integrals; 5.1 The Langevin Equation Revisited; 5.2 Stochastic Differential Equations; 5.3 Which Rule Should Be Used?; 5.4 Some Examples; 6 Functional Integrals; 6.1 Functional Integrals
6.2 The Wiener Integral6.3 Wiener Measure; 6.4 The Feynman-Kac Formula; 6.5 Feynman Path Integrals; 6.6 Evaluation of Wiener Integrals; 6.7 Applications of Functional Integrals; 7 Some Important Special Cases; 7.1 Several Cases of Interest; 7.2 The Free Particle; 7.3 The Distribution of Displacements; 7.4 The Harmonically Bound Particle; 7.5 A Particle in a Constant Force Field; 7.6 The Uniaxial Rotor; 7.7 An Equation for the Distribution of Displacements; 7.8 Discussion; 8 The Smoluchowski Equation; 8.1 The Kramers-Klein Equation; 8.2 The Smoluchowski Equation
8.3 Elimination of Fast Variables8.4 The Smoluchowski Equation Continued; 8.5 Passage over Potential Barriers; 8.6 Concluding Remarks; 9 Random Walk; 9.1 The Random Walk; 9.2 The One-Dimensional Pearson Walk; 9.3 The Biased Random Walk; 9.4 The Persistent Walk; 9.5 Boundaries and First Passage Times; 9.6 Random Remarks on Random Walks; 10 Statistical Mechanics; 10.1 Molecular Distribution Functions; 10.2 The Liouville Equation; 10.3 Projection Operators-The Zwanzig Equation; 10.4 Projection Operators-The Mori Equation; 10.5 Concluding Remarks
11 Stochastic Equations from a Statistical Mechanical Viewpoint11.1 The Langevin Equation A Heuristic View; 11.2 The Fokker-Planck Equation-A Heuristic View; 11.3 What is Wrong with these Derivations?; 11.4 Eliminating Fast Processes; 11.5 The Distribution Function; 11.6 Discussion; 12 Two Exactly Treatable Models; 12.1 Two Illustrative Examples; 12.2 Brownian Motion in a Dilute Gas; 12.3 Discussion; 12.4 The Particle Bound to a Lattice; 12.5 The One-Dimensional Case; 12.6 Discussion; 13 Brownian Motion and Noise; 13.1 Limits on Measurement; 13.2 Oscillations of a Fiber
13.3 A Pneumatic Example
Record Nr. UNINA-9910960525703321
Mazo Robert M  
Oxford, : Clarendon Press, 2002
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Hilbert C Modules and Quantum Markov Semigroups / / by Lunchuan Zhang
Hilbert C Modules and Quantum Markov Semigroups / / by Lunchuan Zhang
Autore Zhang Lunchuan
Edizione [1st ed. 2024.]
Pubbl/distr/stampa Singapore : , : Springer Nature Singapore : , : Imprint : Springer, , 2024
Descrizione fisica 1 online resource (222 pages)
Disciplina 512.55
Soggetto topico Operator theory
Functional analysis
Markov processes
Operator Theory
Functional Analysis
Markov Process
Àlgebres de Hilbert
Mòduls (Àlgebra)
Processos de Markov
Soggetto genere / forma Llibres electrònics
ISBN 981-9986-68-0
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Basic Theory of Hilbert C*-modules -- Kasprove’s Stabilization and Fredholm Generalized Index Theory -- Quantum Markov Semigroups and Operator-valued Dirichlet Forms.
Record Nr. UNINA-9910847579803321
Zhang Lunchuan  
Singapore : , : Springer Nature Singapore : , : Imprint : Springer, , 2024
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Local Limit Theorems for Inhomogeneous Markov Chains [[electronic resource] /] / by Dmitry Dolgopyat, Omri M. Sarig
Local Limit Theorems for Inhomogeneous Markov Chains [[electronic resource] /] / by Dmitry Dolgopyat, Omri M. Sarig
Autore Dolgopyat Dmitry
Edizione [1st ed. 2023.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Springer, , 2023
Descrizione fisica 1 online resource (348 pages)
Disciplina 519.2
Altri autori (Persone) SarigOmri M
Collana Lecture Notes in Mathematics
Soggetto topico Probabilities
Stochastic processes
Dynamical systems
Probability Theory
Stochastic Processes
Dynamical Systems
Teoremes de límit (Teoria de probabilitats)
Processos de Markov
Soggetto genere / forma Llibres electrònics
ISBN 3-031-32601-6
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Acknowledgments -- Contents -- Notation -- 1 Overview -- 1.1 Setup and Aim -- 1.2 The Obstructions to the Local Limit Theorems -- 1.3 How to Show that the Obstructions Do Not Occur -- 1.4 What Happens When the Obstructions Do Occur -- 1.4.1 Lattice Case -- 1.4.2 Center-Tight Case -- 1.4.3 Reducible Case -- 1.5 Some Final Words on the Setup of this Work -- 1.6 Prerequisites -- 1.7 Notes and References -- 2 Markov Arrays, Additive Functionals, and Uniform Ellipticity -- 2.1 The Basic Setup -- 2.1.1 Inhomogeneous Markov Chains -- 2.1.2 Inhomogeneous Markov Arrays -- 2.1.3 Additive Functionals -- 2.2 Uniform Ellipticity -- 2.2.1 The Definition -- 2.2.2 Contraction Estimates and Exponential Mixing -- 2.2.3 Bridge Probabilities -- 2.3 Structure Constants -- 2.3.1 Hexagons -- 2.3.2 Balance and Structure Constants -- 2.3.3 The Ladder Process -- 2.4 γ-Step Ellipticity Conditions -- *2.5 Uniform Ellipticity and Strong Mixing Conditions -- 2.6 Reduction to Point Mass Initial Distributions -- 2.7 Notes and References -- 3 Variance Growth, Center-Tightness, and the CentralLimit Theorem -- 3.1 Main Results -- 3.1.1 Center-Tightness and Variance Growth -- 3.1.2 The Central Limit Theorem and theTwo-Series Theorem -- 3.2 Proofs -- 3.2.1 The Gradient Lemma -- 3.2.2 The Estimate of Var(SN) -- 3.2.3 McLeish's Martingale Central Limit Theorem -- 3.2.4 Proof of the Central Limit Theorem -- 3.2.5 Convergence of Moments -- 3.2.6 Characterization of Center-Tight Additive Functionals -- 3.2.7 Proof of the Two-Series Theorem -- *3.3 The Almost Sure Invariance Principle -- 3.4 Notes and References -- 4 The Essential Range and Irreducibility -- 4.1 Definitions and Motivation -- 4.2 Main Results -- 4.2.1 Markov Chains -- 4.2.2 Markov Arrays -- 4.2.3 Hereditary Arrays -- 4.3 Proofs -- 4.3.1 Reduction Lemma -- 4.3.2 Joint Reduction.
4.3.3 The Possible Values of the Co-Range -- 4.3.4 Calculation of the Essential Range -- 4.3.5 Existence of Irreducible Reductions -- 4.3.6 Characterization of Hereditary Additive Functionals -- 4.4 Notes and References -- 5 The Local Limit Theorem in the Irreducible Case -- 5.1 Main Results -- 5.1.1 Local Limit Theorems for Markov Chains -- 5.1.2 Local Limit Theorems for Markov Arrays -- 5.1.3 Mixing Local Limit Theorems -- 5.2 Proofs -- 5.2.1 Strategy of Proof -- 5.2.2 Characteristic Function Estimates -- 5.2.3 The LLT via Weak Convergence of Measures -- 5.2.4 The LLT in the Irreducible Non-Lattice Case -- 5.2.5 The LLT in the Irreducible Lattice Case -- 5.2.6 Mixing LLT -- 5.3 Notes and References -- 6 The Local Limit Theorem in the Reducible Case -- 6.1 Main Results -- 6.1.1 Heuristics and Warm Up Examples -- 6.1.2 The LLT in the Reducible Case -- 6.1.3 Irreducibility as a Necessary Condition for the Mixing LLT -- 6.1.4 Universal Bounds for Prob[SN-zN(a,b)] -- 6.2 Proofs -- 6.2.1 Characteristic Functions in the Reducible Case -- 6.2.2 Proof of the LLT in the Reducible Case -- 6.2.3 Necessity of the Irreducibility Assumption -- 6.2.4 Universal Bounds for Markov Chains -- 6.2.5 Universal Bounds for Markov Arrays -- 6.3 Notes and References -- 7 Local Limit Theorems for Moderate Deviationsand Large Deviations -- 7.1 Moderate Deviations and Large Deviations -- 7.2 Local Limit Theorems for Large Deviations -- 7.2.1 The Log Moment Generating Functions -- 7.2.2 The Rate Functions -- 7.2.3 The LLT for Moderate Deviations -- 7.2.4 The LLT for Large Deviations -- 7.3 Proofs -- 7.3.1 Strategy of Proof -- 7.3.2 A Parameterized Family of Changes of Measure -- 7.3.3 Choosing the Parameters -- 7.3.4 The Asymptotic Behavior of V"0365VξN(SN) -- 7.3.5 Asymptotics of the Log Moment Generating Functions -- 7.3.6 Asymptotics of the Rate Functions.
7.3.7 Proof of the Local Limit Theorem for Large Deviations -- 7.3.8 Rough Bounds in the Reducible Case -- 7.4 Large Deviations Thresholds -- 7.4.1 The Large Deviations Threshold Theorem -- 7.4.2 Admissible Sequences -- 7.4.3 Proof of the Large Deviations Threshold Theorem -- 7.4.4 Examples -- 7.5 Notes and References -- 8 Important Examples and Special Cases -- 8.1 Introduction -- 8.2 Sums of Independent Random Variables -- 8.3 Homogenous Markov Chains -- *8.4 One-Step Homogeneous Additive Functionals in L2 -- 8.5 Asymptotically Homogeneous Markov Chains -- 8.6 Equicontinuous Additive Functionals -- 8.7 Notes and References -- 9 Local Limit Theorems for Markov Chains in RandomEnvironments -- 9.1 Markov Chains in Random Environments -- 9.1.1 Formal Definitions -- 9.1.2 Examples -- 9.1.3 Conditions and Assumptions -- 9.2 Main Results -- 9.3 Proofs -- 9.3.1 Existence of Stationary Measures -- 9.3.2 The Essential Range is Almost Surely Constant -- 9.3.3 Variance Growth -- 9.3.4 Irreducibility and the LLT -- 9.3.5 LLT for Large Deviations -- 9.4 Notes and References -- A The Gärtner-Ellis Theorem in One Dimension -- A.1 The Statement -- A.2 Background from Convex Analysis -- A.3 Proof of the Gärtner-Ellis Theorem -- A.4 Notes and References -- B Hilbert's Projective Metric and Birkhoff's Theorem -- B.1 Hilbert's Projective Metric -- B.2 Contraction Properties -- B.3 Notes and References -- C Perturbations of Operators with Spectral Gap -- C.1 The Perturbation Theorem -- C.2 Some Facts from Analysis -- C.3 Proof of the Perturbation Theorem -- C.4 Notes and References -- References -- Index.
Record Nr. UNISA-996542671903316
Dolgopyat Dmitry  
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2023
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Local Limit Theorems for Inhomogeneous Markov Chains / / by Dmitry Dolgopyat, Omri M. Sarig
Local Limit Theorems for Inhomogeneous Markov Chains / / by Dmitry Dolgopyat, Omri M. Sarig
Autore Dolgopyat Dmitry
Edizione [1st ed. 2023.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Springer, , 2023
Descrizione fisica 1 online resource (348 pages)
Disciplina 519.2
Altri autori (Persone) SarigOmri M
Collana Lecture Notes in Mathematics
Soggetto topico Probabilities
Stochastic processes
Dynamics
Probability Theory
Stochastic Processes
Dynamical Systems
Teoremes de límit (Teoria de probabilitats)
Processos de Markov
Soggetto genere / forma Llibres electrònics
ISBN 3-031-32601-6
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Acknowledgments -- Contents -- Notation -- 1 Overview -- 1.1 Setup and Aim -- 1.2 The Obstructions to the Local Limit Theorems -- 1.3 How to Show that the Obstructions Do Not Occur -- 1.4 What Happens When the Obstructions Do Occur -- 1.4.1 Lattice Case -- 1.4.2 Center-Tight Case -- 1.4.3 Reducible Case -- 1.5 Some Final Words on the Setup of this Work -- 1.6 Prerequisites -- 1.7 Notes and References -- 2 Markov Arrays, Additive Functionals, and Uniform Ellipticity -- 2.1 The Basic Setup -- 2.1.1 Inhomogeneous Markov Chains -- 2.1.2 Inhomogeneous Markov Arrays -- 2.1.3 Additive Functionals -- 2.2 Uniform Ellipticity -- 2.2.1 The Definition -- 2.2.2 Contraction Estimates and Exponential Mixing -- 2.2.3 Bridge Probabilities -- 2.3 Structure Constants -- 2.3.1 Hexagons -- 2.3.2 Balance and Structure Constants -- 2.3.3 The Ladder Process -- 2.4 γ-Step Ellipticity Conditions -- *2.5 Uniform Ellipticity and Strong Mixing Conditions -- 2.6 Reduction to Point Mass Initial Distributions -- 2.7 Notes and References -- 3 Variance Growth, Center-Tightness, and the CentralLimit Theorem -- 3.1 Main Results -- 3.1.1 Center-Tightness and Variance Growth -- 3.1.2 The Central Limit Theorem and theTwo-Series Theorem -- 3.2 Proofs -- 3.2.1 The Gradient Lemma -- 3.2.2 The Estimate of Var(SN) -- 3.2.3 McLeish's Martingale Central Limit Theorem -- 3.2.4 Proof of the Central Limit Theorem -- 3.2.5 Convergence of Moments -- 3.2.6 Characterization of Center-Tight Additive Functionals -- 3.2.7 Proof of the Two-Series Theorem -- *3.3 The Almost Sure Invariance Principle -- 3.4 Notes and References -- 4 The Essential Range and Irreducibility -- 4.1 Definitions and Motivation -- 4.2 Main Results -- 4.2.1 Markov Chains -- 4.2.2 Markov Arrays -- 4.2.3 Hereditary Arrays -- 4.3 Proofs -- 4.3.1 Reduction Lemma -- 4.3.2 Joint Reduction.
4.3.3 The Possible Values of the Co-Range -- 4.3.4 Calculation of the Essential Range -- 4.3.5 Existence of Irreducible Reductions -- 4.3.6 Characterization of Hereditary Additive Functionals -- 4.4 Notes and References -- 5 The Local Limit Theorem in the Irreducible Case -- 5.1 Main Results -- 5.1.1 Local Limit Theorems for Markov Chains -- 5.1.2 Local Limit Theorems for Markov Arrays -- 5.1.3 Mixing Local Limit Theorems -- 5.2 Proofs -- 5.2.1 Strategy of Proof -- 5.2.2 Characteristic Function Estimates -- 5.2.3 The LLT via Weak Convergence of Measures -- 5.2.4 The LLT in the Irreducible Non-Lattice Case -- 5.2.5 The LLT in the Irreducible Lattice Case -- 5.2.6 Mixing LLT -- 5.3 Notes and References -- 6 The Local Limit Theorem in the Reducible Case -- 6.1 Main Results -- 6.1.1 Heuristics and Warm Up Examples -- 6.1.2 The LLT in the Reducible Case -- 6.1.3 Irreducibility as a Necessary Condition for the Mixing LLT -- 6.1.4 Universal Bounds for Prob[SN-zN(a,b)] -- 6.2 Proofs -- 6.2.1 Characteristic Functions in the Reducible Case -- 6.2.2 Proof of the LLT in the Reducible Case -- 6.2.3 Necessity of the Irreducibility Assumption -- 6.2.4 Universal Bounds for Markov Chains -- 6.2.5 Universal Bounds for Markov Arrays -- 6.3 Notes and References -- 7 Local Limit Theorems for Moderate Deviationsand Large Deviations -- 7.1 Moderate Deviations and Large Deviations -- 7.2 Local Limit Theorems for Large Deviations -- 7.2.1 The Log Moment Generating Functions -- 7.2.2 The Rate Functions -- 7.2.3 The LLT for Moderate Deviations -- 7.2.4 The LLT for Large Deviations -- 7.3 Proofs -- 7.3.1 Strategy of Proof -- 7.3.2 A Parameterized Family of Changes of Measure -- 7.3.3 Choosing the Parameters -- 7.3.4 The Asymptotic Behavior of V"0365VξN(SN) -- 7.3.5 Asymptotics of the Log Moment Generating Functions -- 7.3.6 Asymptotics of the Rate Functions.
7.3.7 Proof of the Local Limit Theorem for Large Deviations -- 7.3.8 Rough Bounds in the Reducible Case -- 7.4 Large Deviations Thresholds -- 7.4.1 The Large Deviations Threshold Theorem -- 7.4.2 Admissible Sequences -- 7.4.3 Proof of the Large Deviations Threshold Theorem -- 7.4.4 Examples -- 7.5 Notes and References -- 8 Important Examples and Special Cases -- 8.1 Introduction -- 8.2 Sums of Independent Random Variables -- 8.3 Homogenous Markov Chains -- *8.4 One-Step Homogeneous Additive Functionals in L2 -- 8.5 Asymptotically Homogeneous Markov Chains -- 8.6 Equicontinuous Additive Functionals -- 8.7 Notes and References -- 9 Local Limit Theorems for Markov Chains in RandomEnvironments -- 9.1 Markov Chains in Random Environments -- 9.1.1 Formal Definitions -- 9.1.2 Examples -- 9.1.3 Conditions and Assumptions -- 9.2 Main Results -- 9.3 Proofs -- 9.3.1 Existence of Stationary Measures -- 9.3.2 The Essential Range is Almost Surely Constant -- 9.3.3 Variance Growth -- 9.3.4 Irreducibility and the LLT -- 9.3.5 LLT for Large Deviations -- 9.4 Notes and References -- A The Gärtner-Ellis Theorem in One Dimension -- A.1 The Statement -- A.2 Background from Convex Analysis -- A.3 Proof of the Gärtner-Ellis Theorem -- A.4 Notes and References -- B Hilbert's Projective Metric and Birkhoff's Theorem -- B.1 Hilbert's Projective Metric -- B.2 Contraction Properties -- B.3 Notes and References -- C Perturbations of Operators with Spectral Gap -- C.1 The Perturbation Theorem -- C.2 Some Facts from Analysis -- C.3 Proof of the Perturbation Theorem -- C.4 Notes and References -- References -- Index.
Record Nr. UNINA-9910736025503321
Dolgopyat Dmitry  
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2023
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Markov chains on metric spaces : a short course / / Michel Benaim, Tobias Hurth
Markov chains on metric spaces : a short course / / Michel Benaim, Tobias Hurth
Autore Benaim Michel
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , 2022
Descrizione fisica 1 online resource (205 pages)
Disciplina 519.233
Collana Universitext
Soggetto topico Markov processes
Metric spaces
Processos de Markov
Espais mètrics
Soggetto genere / forma Llibres electrònics
ISBN 3-031-11822-7
9783031118210
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Contents -- Preliminaries -- 1 Markov Chains -- 1.1 Markov Kernels -- 1.2 Markov Chains -- 1.3 The Canonical Chain -- 1.4 Markov and Strong Markov Properties -- 1.5 Continuous Time: Markov Processes -- 2 Countable Markov Chains -- 2.1 Recurrence and Transience -- 2.1.1 Positive Recurrence -- 2.1.2 Null Recurrence -- 2.2 Subsets of Recurrent Sets -- 2.3 Recurrence and Lyapunov Functions -- 2.4 Aperiodic Chains -- 2.5 The Convergence Theorem -- 2.6 Application to Renewal Theory -- 2.6.1 Coupling of Renewal Processes -- 2.7 Convergence Rates for Positive Recurrent Chains -- Notes -- 3 Random Dynamical Systems -- 3.1 General Definitions -- 3.2 Representation of Markov Chains by RDS -- Notes -- 4 Invariant and Ergodic Probability Measures -- 4.1 Weak Convergence of Probability Measures -- 4.1.1 Tightness and Prohorov's Theorem -- A Tightness Criterion -- 4.2 Invariant Measures -- 4.2.1 Tightness Criteria for Empirical Occupation Measures -- 4.3 Excessive Measures -- 4.4 Ergodic Measures -- 4.5 Unique Ergodicity -- 4.5.1 Unique Ergodicity of Random Contractions -- 4.6 Classical Results from Ergodic Theory -- 4.6.1 Poincaré, Birkhoff, and Ergodic Decomposition Theorems -- 4.7 Application to Markov Chains -- 4.8 Continuous Time: Invariant Probabilities for Markov Processes -- Notes -- 5 Irreducibility -- 5.1 Resolvent and ξ-Irreducibility -- 5.2 The Accessible Set -- 5.2.1 Continuous Time: Accessibility -- 5.3 The Asymptotic Strong Feller Property -- 5.3.1 Strong Feller Implies Asymptotic Strong Feller -- 5.3.2 A Sufficient Condition for the Asymptotic Strong Feller Property -- 5.3.3 Unique Ergodicity of Asymptotic Strong Feller Chains -- Notes -- 6 Petite Sets and Doeblin Points -- 6.1 Petite Sets, Small Sets, Doeblin Points -- 6.1.1 Continuous Time: Doeblin Points for Markov Processes -- 6.2 Random Dynamical Systems.
6.3 Random Switching Between Vector Fields -- 6.3.1 The Weak Bracket Condition -- 6.4 Piecewise Deterministic Markov Processes -- 6.4.1 Invariant Measures -- 6.4.2 The Strong Bracket Condition -- 6.5 Stochastic Differential Equations -- 6.5.1 Accessibility -- 6.5.2 Hörmander Conditions -- Notes -- 7 Harris and Positive Recurrence -- 7.1 Stability and Positive Recurrence -- 7.2 Harris Recurrence -- 7.2.1 Petite Sets and Harris Recurrence -- 7.3 Recurrence Criteria and Lyapunov Functions -- 7.4 Subsets of Recurrent Sets -- 7.5 Petite Sets and Positive Recurrence -- 7.6 Positive Recurrence for Feller Chains -- 7.6.1 Application to PDMPs -- 7.6.2 Application to SDEs -- 8 Harris Ergodic Theorem -- 8.1 Total Variation Distance -- 8.1.1 Coupling -- 8.2 Harris Convergence Theorems -- 8.2.1 Geometric Convergence -- Aperiodic Small Sets -- 8.2.2 Continuous Time: Exponential Convergence -- 8.2.3 Coupling, Splitting, and Polynomial Convergence -- 8.3 Convergence in Wasserstein Distance -- A Monotone Class and Martingales -- A.1 Monotone Class Theorem -- A.2 Conditional Expectation -- A.3 Martingales -- Bibliography -- List of Symbols -- List of Symbols -- Index.
Record Nr. UNINA-9910632475603321
Benaim Michel  
Cham, Switzerland : , : Springer, , 2022
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Markov chains on metric spaces : a short course / / Michel Benaim, Tobias Hurth
Markov chains on metric spaces : a short course / / Michel Benaim, Tobias Hurth
Autore Benaim Michel
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , 2022
Descrizione fisica 1 online resource (205 pages)
Disciplina 519.233
Collana Universitext
Soggetto topico Markov processes
Metric spaces
Processos de Markov
Espais mètrics
Soggetto genere / forma Llibres electrònics
ISBN 3-031-11822-7
9783031118210
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Contents -- Preliminaries -- 1 Markov Chains -- 1.1 Markov Kernels -- 1.2 Markov Chains -- 1.3 The Canonical Chain -- 1.4 Markov and Strong Markov Properties -- 1.5 Continuous Time: Markov Processes -- 2 Countable Markov Chains -- 2.1 Recurrence and Transience -- 2.1.1 Positive Recurrence -- 2.1.2 Null Recurrence -- 2.2 Subsets of Recurrent Sets -- 2.3 Recurrence and Lyapunov Functions -- 2.4 Aperiodic Chains -- 2.5 The Convergence Theorem -- 2.6 Application to Renewal Theory -- 2.6.1 Coupling of Renewal Processes -- 2.7 Convergence Rates for Positive Recurrent Chains -- Notes -- 3 Random Dynamical Systems -- 3.1 General Definitions -- 3.2 Representation of Markov Chains by RDS -- Notes -- 4 Invariant and Ergodic Probability Measures -- 4.1 Weak Convergence of Probability Measures -- 4.1.1 Tightness and Prohorov's Theorem -- A Tightness Criterion -- 4.2 Invariant Measures -- 4.2.1 Tightness Criteria for Empirical Occupation Measures -- 4.3 Excessive Measures -- 4.4 Ergodic Measures -- 4.5 Unique Ergodicity -- 4.5.1 Unique Ergodicity of Random Contractions -- 4.6 Classical Results from Ergodic Theory -- 4.6.1 Poincaré, Birkhoff, and Ergodic Decomposition Theorems -- 4.7 Application to Markov Chains -- 4.8 Continuous Time: Invariant Probabilities for Markov Processes -- Notes -- 5 Irreducibility -- 5.1 Resolvent and ξ-Irreducibility -- 5.2 The Accessible Set -- 5.2.1 Continuous Time: Accessibility -- 5.3 The Asymptotic Strong Feller Property -- 5.3.1 Strong Feller Implies Asymptotic Strong Feller -- 5.3.2 A Sufficient Condition for the Asymptotic Strong Feller Property -- 5.3.3 Unique Ergodicity of Asymptotic Strong Feller Chains -- Notes -- 6 Petite Sets and Doeblin Points -- 6.1 Petite Sets, Small Sets, Doeblin Points -- 6.1.1 Continuous Time: Doeblin Points for Markov Processes -- 6.2 Random Dynamical Systems.
6.3 Random Switching Between Vector Fields -- 6.3.1 The Weak Bracket Condition -- 6.4 Piecewise Deterministic Markov Processes -- 6.4.1 Invariant Measures -- 6.4.2 The Strong Bracket Condition -- 6.5 Stochastic Differential Equations -- 6.5.1 Accessibility -- 6.5.2 Hörmander Conditions -- Notes -- 7 Harris and Positive Recurrence -- 7.1 Stability and Positive Recurrence -- 7.2 Harris Recurrence -- 7.2.1 Petite Sets and Harris Recurrence -- 7.3 Recurrence Criteria and Lyapunov Functions -- 7.4 Subsets of Recurrent Sets -- 7.5 Petite Sets and Positive Recurrence -- 7.6 Positive Recurrence for Feller Chains -- 7.6.1 Application to PDMPs -- 7.6.2 Application to SDEs -- 8 Harris Ergodic Theorem -- 8.1 Total Variation Distance -- 8.1.1 Coupling -- 8.2 Harris Convergence Theorems -- 8.2.1 Geometric Convergence -- Aperiodic Small Sets -- 8.2.2 Continuous Time: Exponential Convergence -- 8.2.3 Coupling, Splitting, and Polynomial Convergence -- 8.3 Convergence in Wasserstein Distance -- A Monotone Class and Martingales -- A.1 Monotone Class Theorem -- A.2 Conditional Expectation -- A.3 Martingales -- Bibliography -- List of Symbols -- List of Symbols -- Index.
Record Nr. UNISA-996499868703316
Benaim Michel  
Cham, Switzerland : , : Springer, , 2022
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Markov processes and quantum theory / / Masao Nagasawa
Markov processes and quantum theory / / Masao Nagasawa
Autore Nagasawa Masao <1933 August 1->
Pubbl/distr/stampa Cham, Switzerland : , : Birkhäuser, , [2021]
Descrizione fisica 1 online resource (349 pages)
Disciplina 530.12
Collana Monographs in mathematics
Soggetto topico Quantum theory
Teoria quàntica
Processos de Markov
Soggetto genere / forma Llibres electrònics
ISBN 3-030-62688-1
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Contents -- Chapter 1 Mechanics of Random Motion -- 1.1 Smooth Motion and Random Motion -- 1.2 On Stochastic Processes -- 1.3 Itô's Path Analysis -- 1.4 Equation of Motion for a Stochastic Process -- 1.5 Kinematics of Random Motion -- 1.6 Free Random Motion of a Particle -- 1.7 Hooke's Force -- 1.8 Hooke's Force and an Additional Potential -- 1.9 Complex Evolution Functions -- 1.10 Superposition Principle -- 1.11 Entangled Quantum Bit -- 1.12 Light Emission from a Silicon Semiconductor -- 1.13 The Double-Slit Problem -- 1.14 Double-Slit Experiment with Photons -- 1.15 Theory of Photons -- 1.16 Principle of Least Action -- 1.17 Transformation of Probability Measures -- 1.18 Schrödinger Equation and Path Equation -- Chapter 2 Applications -- 2.1 Motion induced by the Coulomb Potential -- 2.2 Charged Particle in a Magnetic Field -- 2.3 Aharonov-Bohm Effect -- 2.4 Tunnel Effect -- 2.5 Bose-Einstein Distribution -- 2.6 Random Motion and the Light Cone -- 2.7 Origin of the Universe -- 2.8 Classification of Boundary Points -- 2.9 Particle Theory of Electron Holography -- 2.10 Escherichia coli and Meson models -- 2.11 High-Temperature Superconductivity -- Chapter 3 Momentum, Kinetic Energy, Locality -- 3.1 Momentum and Kinetic Energy -- 3.2 Matrix Mechanics -- 3.3 Function Representations of Operators -- 3.4 Expectation and Variance -- 3.5 The Heisenberg Uncertainty Principle -- 3.6 Kinetic Energy and Variance of Position -- 3.7 Theory of Hidden Variables -- 3.8 Einstein's Locality -- 3.9 Bell's Inequality -- 3.10 Local Spin Correlation Model -- 3.11 Long-Lasting Controversy and Random Motion -- Chapter 4 Markov Processes -- 4.1 Time-Homogeneous Markov Proces-ses -- 4.2 Transformations by M-Functionals -- 4.3 Change of Time Scale -- 4.4 Duality and Time Reversal -- 4.5 Time Reversal, Last Occurrence Time.
4.6 Time Reversal, Equations of Motion -- 4.7 Conditional Expectation -- 4.8 Paths of Brownian Motion -- Chapter 5 Applications of Relative Entropy -- 5.1 Relative Entropy -- 5.2 Variational Principle -- 5.3 Exponential Family of Distributions -- 5.4 Existence of Entrance and Exit Functions -- 5.5 Cloud of Paths -- 5.6 Kac's Phenomenon of Propagation of Chaos -- Chapter 6 Extinction and Creation -- 6.1 Extinction of Particles -- 6.2 Piecing-Together Markov Processes -- 6.3 Branching Markov Processes -- 6.4 Construction of Branching Markov Processes -- 6.5 Markov Processes with Age -- 6.6 Branching Markov Processes with Age -- Bibliography -- Index.
Record Nr. UNISA-996466405103316
Nagasawa Masao <1933 August 1->  
Cham, Switzerland : , : Birkhäuser, , [2021]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Markov processes and quantum theory / / Masao Nagasawa
Markov processes and quantum theory / / Masao Nagasawa
Autore Nagasawa Masao <1933 August 1->
Pubbl/distr/stampa Cham, Switzerland : , : Birkhäuser, , [2021]
Descrizione fisica 1 online resource (349 pages)
Disciplina 530.12
Collana Monographs in mathematics
Soggetto topico Quantum theory
Teoria quàntica
Processos de Markov
Soggetto genere / forma Llibres electrònics
ISBN 3-030-62688-1
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Contents -- Chapter 1 Mechanics of Random Motion -- 1.1 Smooth Motion and Random Motion -- 1.2 On Stochastic Processes -- 1.3 Itô's Path Analysis -- 1.4 Equation of Motion for a Stochastic Process -- 1.5 Kinematics of Random Motion -- 1.6 Free Random Motion of a Particle -- 1.7 Hooke's Force -- 1.8 Hooke's Force and an Additional Potential -- 1.9 Complex Evolution Functions -- 1.10 Superposition Principle -- 1.11 Entangled Quantum Bit -- 1.12 Light Emission from a Silicon Semiconductor -- 1.13 The Double-Slit Problem -- 1.14 Double-Slit Experiment with Photons -- 1.15 Theory of Photons -- 1.16 Principle of Least Action -- 1.17 Transformation of Probability Measures -- 1.18 Schrödinger Equation and Path Equation -- Chapter 2 Applications -- 2.1 Motion induced by the Coulomb Potential -- 2.2 Charged Particle in a Magnetic Field -- 2.3 Aharonov-Bohm Effect -- 2.4 Tunnel Effect -- 2.5 Bose-Einstein Distribution -- 2.6 Random Motion and the Light Cone -- 2.7 Origin of the Universe -- 2.8 Classification of Boundary Points -- 2.9 Particle Theory of Electron Holography -- 2.10 Escherichia coli and Meson models -- 2.11 High-Temperature Superconductivity -- Chapter 3 Momentum, Kinetic Energy, Locality -- 3.1 Momentum and Kinetic Energy -- 3.2 Matrix Mechanics -- 3.3 Function Representations of Operators -- 3.4 Expectation and Variance -- 3.5 The Heisenberg Uncertainty Principle -- 3.6 Kinetic Energy and Variance of Position -- 3.7 Theory of Hidden Variables -- 3.8 Einstein's Locality -- 3.9 Bell's Inequality -- 3.10 Local Spin Correlation Model -- 3.11 Long-Lasting Controversy and Random Motion -- Chapter 4 Markov Processes -- 4.1 Time-Homogeneous Markov Proces-ses -- 4.2 Transformations by M-Functionals -- 4.3 Change of Time Scale -- 4.4 Duality and Time Reversal -- 4.5 Time Reversal, Last Occurrence Time.
4.6 Time Reversal, Equations of Motion -- 4.7 Conditional Expectation -- 4.8 Paths of Brownian Motion -- Chapter 5 Applications of Relative Entropy -- 5.1 Relative Entropy -- 5.2 Variational Principle -- 5.3 Exponential Family of Distributions -- 5.4 Existence of Entrance and Exit Functions -- 5.5 Cloud of Paths -- 5.6 Kac's Phenomenon of Propagation of Chaos -- Chapter 6 Extinction and Creation -- 6.1 Extinction of Particles -- 6.2 Piecing-Together Markov Processes -- 6.3 Branching Markov Processes -- 6.4 Construction of Branching Markov Processes -- 6.5 Markov Processes with Age -- 6.6 Branching Markov Processes with Age -- Bibliography -- Index.
Record Nr. UNINA-9910488723503321
Nagasawa Masao <1933 August 1->  
Cham, Switzerland : , : Birkhäuser, , [2021]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Markov Renewal and Piecewise Deterministic Processes [[electronic resource] /] / by Christiane Cocozza-Thivent
Markov Renewal and Piecewise Deterministic Processes [[electronic resource] /] / by Christiane Cocozza-Thivent
Autore Cocozza-Thivent Christiane
Edizione [1st ed. 2021.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Springer, , 2021
Descrizione fisica 1 online resource (XIV, 252 p. 16 illus., 4 illus. in color.)
Disciplina 519.233
Collana Probability Theory and Stochastic Modelling
Soggetto topico Markov processes
Computer science - Mathematics
Mathematical statistics
Markov Process
Probability and Statistics in Computer Science
Processos de Markov
Estadística matemàtica
Soggetto genere / forma Llibres electrònics
ISBN 3-030-70447-5
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Tools -- Markov renewal processes and related processes -- First steps with PDMP -- Hitting time distribution -- Intensity of some marked point pocesses -- Generalized Kolmogorov equations -- A martingale approach -- Stability -- Numerical methods -- Switching Processes -- Tools -- Interarrival distribution with several Dirac measures -- Algorithm convergence's proof.
Record Nr. UNISA-996466393303316
Cocozza-Thivent Christiane  
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2021
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Markov Renewal and Piecewise Deterministic Processes / / by Christiane Cocozza-Thivent
Markov Renewal and Piecewise Deterministic Processes / / by Christiane Cocozza-Thivent
Autore Cocozza-Thivent Christiane
Edizione [1st ed. 2021.]
Pubbl/distr/stampa Cham : , : Springer International Publishing : , : Imprint : Springer, , 2021
Descrizione fisica 1 online resource (XIV, 252 p. 16 illus., 4 illus. in color.)
Disciplina 519.233
Collana Probability Theory and Stochastic Modelling
Soggetto topico Markov processes
Computer science - Mathematics
Mathematical statistics
Markov Process
Probability and Statistics in Computer Science
Processos de Markov
Estadística matemàtica
Soggetto genere / forma Llibres electrònics
ISBN 3-030-70447-5
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Tools -- Markov renewal processes and related processes -- First steps with PDMP -- Hitting time distribution -- Intensity of some marked point pocesses -- Generalized Kolmogorov equations -- A martingale approach -- Stability -- Numerical methods -- Switching Processes -- Tools -- Interarrival distribution with several Dirac measures -- Algorithm convergence's proof.
Record Nr. UNINA-9910484004403321
Cocozza-Thivent Christiane  
Cham : , : Springer International Publishing : , : Imprint : Springer, , 2021
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui