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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 | ||
| ||
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. | UNINA-9910736025503321 |
|
Dolgopyat Dmitry
|
||
| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2023 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
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 | ||
| ||
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 | ||
| ||
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 | ||
| ||
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 |
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Nagasawa Masao <1933 August 1->
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| Cham, Switzerland : , : Birkhäuser, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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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. | UNINA-9910484004403321 |
|
Cocozza-Thivent Christiane
|
||
| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2021 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
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 | ||
| ||
MCMC from scratch : a practical introduction to Markov Chain Monte Carlo / / Masanori Hanada and So Matsuura
| MCMC from scratch : a practical introduction to Markov Chain Monte Carlo / / Masanori Hanada and So Matsuura |
| Autore | Hanada Masanori |
| Pubbl/distr/stampa | Singapore : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (198 pages) |
| Disciplina | 530.12 |
| Soggetto topico |
Markov processes
Processos de Markov |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 981-19-2715-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910619274803321 |
|
Hanada Masanori
|
||
| Singapore : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
MCMC from scratch : a practical introduction to Markov Chain Monte Carlo / / Masanori Hanada and So Matsuura
| MCMC from scratch : a practical introduction to Markov Chain Monte Carlo / / Masanori Hanada and So Matsuura |
| Autore | Hanada Masanori |
| Pubbl/distr/stampa | Singapore : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (198 pages) |
| Disciplina | 530.12 |
| Soggetto topico |
Markov processes
Processos de Markov |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 981-19-2715-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISA-996495168903316 |
|
Hanada Masanori
|
||
| Singapore : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
