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Applied Linear Algebra, Probability and Statistics [[electronic resource] ] : A Volume in Honour of C. R. Rao and Arbind K. Lal / / edited by Ravindra B. Bapat, Manjunatha Prasad Karantha, Stephen J. Kirkland, Samir Kumar Neogy, Sukanta Pati, Simo Puntanen
| Applied Linear Algebra, Probability and Statistics [[electronic resource] ] : A Volume in Honour of C. R. Rao and Arbind K. Lal / / edited by Ravindra B. Bapat, Manjunatha Prasad Karantha, Stephen J. Kirkland, Samir Kumar Neogy, Sukanta Pati, Simo Puntanen |
| Autore | Bapat Ravindra B |
| Edizione | [1st ed. 2023.] |
| Pubbl/distr/stampa | Singapore : , : Springer Nature Singapore : , : Imprint : Springer, , 2023 |
| Descrizione fisica | 1 online resource (540 pages) |
| Disciplina | 512.5 |
| Altri autori (Persone) |
KaranthaManjunatha Prasad
KirklandStephen J NeogySamir Kumar PatiSukanta PuntanenSimo |
| Collana | Indian Statistical Institute Series |
| Soggetto topico |
Algebras, Linear
Probabilities Statistics Graph theory Stochastic processes Game theory Linear Algebra Probability Theory Statistical Theory and Methods Graph Theory Stochastic Processes Game Theory |
| ISBN | 981-9923-10-7 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Chapter 1. On Some Matrix Versions of Covariance, Harmonic Mean and other Inequalities: An Overview -- Chapter 2. The Impact of Professor C. R. Rao's Research used in solving problems in Applied Probability -- Chapter 3. Upper ounds for the Euclidean distances between the BLUEs under the partitioned linear fixed model and the corresponding mixed model -- Chapter 4. Nucleolus Computation for some Structured TU Games via Graph Theory and Linear Algebra -- Chapter 5. From Linear System of Equations to Artificial Intelligence - The evolution Journey of Computer Tomographic Image Reconstruction Algorithms -- Chapter 6. Shapley Value and other Axiomatic Extensions to Shapley Value -- Chapter 7. An Accelerated Block Randomized Kaczmarz Methos -- Chapter 8. Nullity of Graphs - A Survey and Some New Results -- Chapter 9. Some Observations on Algebraic Connectivity of Graphs -- Chapter 10. Orthogonality for iadjoints f Operators -- Chapter 11. Permissible covariance structures for simultaneous retention of BLUEs in small and big linear models -- Chapter 12. On some Special Matrices and its Applications in Linear Complementarity Problem -- Chapter 3. On Nearest Matrix with Partially Specified Eigen Structure -- Chapter 14. Equality of BLUEs for Full, Small, and Intermediate Linear Models under Covariance Change, with links to Data Confidentiality and Encryption.-Chapter 15. Statistical Inference for Middle Censored Data with Applications. etc. |
| Record Nr. | UNINA-9910736008903321 |
Bapat Ravindra B
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| Singapore : , : Springer Nature Singapore : , : Imprint : Springer, , 2023 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Applied stochastic models in business and industry
| Applied stochastic models in business and industry |
| Pubbl/distr/stampa | [Chichester], : John Wiley & Sons, ©1999- |
| Descrizione fisica | 1 online resource |
| Disciplina | 519 |
| Soggetto topico |
Stochastic analysis
Stochastic processes Business mathematics Finance - Mathematical models Industrial management - Mathematical models Industrial statistics Commercial statistics Analyse stochastique Processus stochastiques Statistique industrielle Statistique commerciale Mathématiques financières Finances - Modèles mathématiques Gestion d'entreprise - Modèles mathématiques Business (General) Decision Science Stochastic Processes Industrial Management |
| Soggetto genere / forma | Periodicals. |
| Soggetto non controllato | Mathematical Statistics |
| ISSN | 1526-4025 |
| Formato | Materiale a stampa |
| Livello bibliografico | Periodico |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910139448503321 |
| [Chichester], : John Wiley & Sons, ©1999- | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Applied stochastic models in business and industry
| Applied stochastic models in business and industry |
| Pubbl/distr/stampa | [Chichester], : John Wiley & Sons, ©1999- |
| Descrizione fisica | 1 online resource |
| Disciplina | 519 |
| Soggetto topico |
Stochastic analysis
Stochastic processes Business mathematics Finance - Mathematical models Industrial management - Mathematical models Industrial statistics Commercial statistics Analyse stochastique Processus stochastiques Statistique industrielle Statistique commerciale Mathématiques financières Finances - Modèles mathématiques Gestion d'entreprise - Modèles mathématiques Business (General) Decision Science Stochastic Processes Industrial Management |
| Soggetto genere / forma | Periodicals. |
| Soggetto non controllato | Mathematical Statistics |
| ISSN | 1526-4025 |
| Formato | Materiale a stampa |
| Livello bibliografico | Periodico |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISA-996211928803316 |
| [Chichester], : John Wiley & Sons, ©1999- | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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Discrete-Time Semi-Markov Random Evolutions and Their Applications [[electronic resource] /] / by Nikolaos Limnios, Anatoliy Swishchuk
| Discrete-Time Semi-Markov Random Evolutions and Their Applications [[electronic resource] /] / by Nikolaos Limnios, Anatoliy Swishchuk |
| Autore | Limnios Nikolaos |
| Edizione | [1st ed. 2023.] |
| Pubbl/distr/stampa | Cham : , : Springer Nature Switzerland : , : Imprint : Birkhäuser, , 2023 |
| Descrizione fisica | 1 online resource (206 pages) |
| Disciplina | 519.233 |
| Altri autori (Persone) | SwishchukAnatoliy |
| Collana | Probability and Its Applications |
| Soggetto topico |
Stochastic processes
Probabilities Mathematical statistics Dynamical systems Stochastic Processes Probability Theory Mathematical Statistics Applied Probability Dynamical Systems Stochastic Systems and Control |
| ISBN | 3-031-33429-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- Acronyms -- Notation -- 1 Discrete-Time Stochastic Calculus in Banach Space -- 1.1 Introduction -- 1.2 Random Elements and Discrete-Time Martingales in a Banach Space -- 1.3 Martingale Characterization of Markov and Semi-Markov Chains -- 1.3.1 Martingale Characterization of Markov Chains -- 1.3.2 Martingale Characterization of Markov Processes -- 1.3.3 Martingale Characterization of Semi-Markov Processes -- 1.4 Operator Semigroups and Their Generators -- 1.5 Martingale Problem in a Banach Space -- 1.6 Weak Convergence in a Banach Space -- 1.7 Reducible-Invertible Operators and Their Perturbations -- 1.7.1 Reducible-Invertible Operators -- 1.7.2 Perturbation of Reducible-Invertible Operators -- 2 Discrete-Time Semi-Markov Chains -- 2.1 Introduction -- 2.2 Semi-Markov Chains -- 2.2.1 Definitions -- 2.2.2 Classification of States -- 2.2.3 Markov Renewal Equation and Theorem -- 2.3 Discrete- and Continuous-Time Connection -- 2.4 Compensating Operator and Martingales -- 2.5 Stationary Phase Merging -- 2.6 Semi-Markov Chains in Merging State Space -- 2.6.1 The Ergodic Case -- 2.6.2 The Non-ergodic Case -- 2.7 Concluding Remarks -- 3 Discrete-Time Semi-Markov Random Evolutions -- 3.1 Introduction -- 3.2 Discrete-time Random Evolution with Underlying Markov Chain -- 3.3 Definition and Properties of DTSMRE -- 3.4 Discrete-Time Stochastic Systems -- 3.4.1 Additive Functionals -- 3.4.2 Geometric Markov Renewal Chains -- 3.4.3 Dynamical Systems -- 3.5 Discrete-Time Stochastic Systems in Series Scheme -- 3.6 Concluding Remarks -- 4 Weak Convergence of DTSMRE in Series Scheme -- 4.1 Introduction -- 4.2 Weak Convergence Results -- 4.2.1 Averaging -- 4.2.2 Diffusion Approximation -- 4.2.3 Normal Deviations -- 4.2.4 Rates of Convergence in the Limit Theorems -- 4.3 Proof of Theorems -- 4.3.1 Proof of Theorem 4.1.
4.3.2 Proof of Theorem 4.2 -- 4.3.3 Proof of Theorem 4.3 -- 4.3.4 Proof of Proposition 4.1 -- 4.4 Applications of the Limit Theorems to Stochastic Systems -- 4.4.1 Additive Functionals -- 4.4.2 Geometric Markov Renewal Processes -- 4.4.3 Dynamical Systems -- 4.4.4 Estimation of the Stationary Distribution -- 4.4.5 U-Statistics -- 4.4.6 Rates of Convergence for Stochastic Systems -- 4.5 Concluding Remarks -- 5 DTSMRE in Reduced Random Media -- 5.1 Introduction -- 5.2 Definition and Properties -- 5.3 Average and Diffusion Approximation -- 5.3.1 Averaging -- 5.3.2 Diffusion Approximation -- 5.3.3 Normal Deviations -- 5.4 Proof of Theorems -- 5.4.1 Proof of Theorem 5.1 -- 5.4.2 Proof of Theorem 5.2 -- 5.5 Application to Stochastic Systems -- 5.5.1 Additive Functionals -- 5.5.2 Dynamical Systems -- 5.5.3 Geometric Markov Renewal Chains -- 5.5.4 U-Statistics -- 5.6 Concluding Remarks -- 6 Controlled Discrete-Time Semi-Markov Random Evolutions -- 6.1 Introduction -- 6.2 Controlled Discrete-Time Semi-Markov Random Evolutions -- 6.2.1 Definition of CDTSMREs -- 6.2.2 Examples -- 6.2.3 Dynamic Programming for Controlled Models -- 6.3 Limit Theorems for Controlled Semi-Markov Random Evolutions -- 6.3.1 Averaging of CDTSMREs -- 6.3.2 Diffusion Approximation of DTSMREs -- 6.3.3 Normal Approximation -- 6.4 Applications to Stochastic Systems -- 6.4.1 Controlled Additive Functionals -- 6.4.2 Controlled Geometric Markov Renewal Processes -- 6.4.3 Controlled Dynamical Systems -- 6.4.4 The Dynamic Programming Equations for Limiting Models in Diffusion Approximation -- 6.4.4.1 DPE/HJB Equation for the Limiting CAF in DA (see Sect.6.4.1) -- 6.4.4.2 DPE/HJB Equation for the Limiting CGMRP in DA (see Sect.6.4.2) -- 6.4.4.3 DPE/HJB Equation for the Limiting CDS in DA (see Sect.6.4.3) -- 6.5 Solution of Merton Problem for the Limiting CGMRP in DA -- 6.5.1 Introduction. 6.5.2 Utility Function -- 6.5.3 Value Function or Performance Criterion -- 6.5.4 Solution of Merton Problem: Examples -- 6.5.5 Solution of Merton Problem -- 6.6 Rates of Convergence in Averaging and Diffusion Approximations -- 6.7 Proofs -- 6.7.1 Proof of Theorem 6.1 -- 6.7.2 Proof of Theorem 6.2 -- 6.7.3 Proof of Theorem 6.3 -- 6.7.4 Proof of Proposition 6.1 -- 6.8 Concluding Remarks -- 7 Epidemic Models in Random Media -- 7.1 Introduction -- 7.2 From the Deterministic to Stochastic SARS Model -- 7.3 Averaging of Stochastic SARS Models -- 7.4 SARS Model in Merging Semi-Markov Random Media -- 7.5 Diffusion Approximation of Stochastic SARS Models in Semi-Markov Random Media -- 7.6 Concluding remarks -- 8 Optimal Stopping of Geometric Markov Renewal Chains and Pricing -- 8.1 Introduction -- 8.2 GMRC and Embedded Markov-Modulated (B,S)-Security Markets -- 8.2.1 Definition of the GMRC -- 8.2.2 Statement of the Problem: Optimal Stopping Rule -- 8.3 GMRP as Jump Discrete-Time Semi-Markov Random Evolution -- 8.4 Martingale Properties of GMRC -- 8.5 Optimal Stopping Rules for GMRC -- 8.6 Martingale Properties of Discount Price and Discount Capital -- 8.7 American Option Pricing Formulae for embedded Markov-modulated (B,S)-Security markets -- 8.8 European Option Pricing Formula for Embedded Markov-Modulated (B,S)-Security Markets -- 8.9 Proof of Theorems -- 8.10 Concluding Remarks -- A Markov Chains -- A.1 Transition Function -- A.2 Irreducible Markov Chains -- A.3 Recurrent Markov Chains -- A.4 Invariant Measures -- A.5 Uniformly Ergodic Markov Chains -- Bibliography -- Index. |
| Record Nr. | UNINA-9910735778203321 |
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Limnios Nikolaos
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| Cham : , : Springer Nature Switzerland : , : Imprint : Birkhäuser, , 2023 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Facets of Noise [[electronic resource] ] : Effects in Classical and Quantum Systems / / by Debraj Das, Shamik Gupta
| Facets of Noise [[electronic resource] ] : Effects in Classical and Quantum Systems / / by Debraj Das, Shamik Gupta |
| Autore | Das Debraj |
| Edizione | [1st ed. 2023.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2023 |
| Descrizione fisica | 1 online resource (420 pages) |
| Disciplina | 530.13 |
| Altri autori (Persone) |
GuptaShamik
Jona-LasinioGiovanni |
| Collana | Fundamental Theories of Physics |
| Soggetto topico |
Statistical Physics
Stochastic processes Acoustical engineering Quantum physics Stochastic Processes Engineering Acoustics Quantum Physics |
| ISBN | 3-031-45312-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Random variables and probability distributions -- Stochastic processes -- Kinetic theory -- Statistical mechanics -- Nonlinear dynamics -- Stationary correlations in the noisy Kuramoto model -- Bifurcation behavior of a nonlinear system by introducing noise -- Relaxation dynamics of mean-field classical spin systems -- Critical exponents in mean-field classical spin systems -- Quantum systems subject to random projective measurements. |
| Record Nr. | UNINA-9910831009203321 |
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Das Debraj
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| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2023 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Finance and stochastics
| Finance and stochastics |
| Pubbl/distr/stampa | Berlin, : Springer |
| Descrizione fisica | 1 online resource |
| Disciplina | 332 |
| Soggetto topico |
Finance - Mathematical models
Stochastic analysis Finances - Modèles mathématiques Analyse stochastique Banking, Finance & Investing Stochastic Processes Kreditmarkt Stochastisches Modell Finanzstatistik Zeitschrift Online-Ressource Financiën Stochastische methoden |
| Soggetto genere / forma |
Periodicals.
Zeitschrift Online-Publikation |
| Soggetto non controllato | Banking |
| ISSN | 1432-1122 |
| Formato | Materiale a stampa |
| Livello bibliografico | Periodico |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISA-996211818603316 |
| Berlin, : Springer | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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Finance and stochastics
| Finance and stochastics |
| Pubbl/distr/stampa | Berlin, : Springer |
| Descrizione fisica | 1 online resource |
| Disciplina | 332 |
| Soggetto topico |
Finance - Mathematical models
Stochastic analysis Finances - Modèles mathématiques Analyse stochastique Banking, Finance & Investing Stochastic Processes Kreditmarkt Stochastisches Modell Finanzstatistik Zeitschrift Online-Ressource Financiën Stochastische methoden |
| Soggetto genere / forma |
Periodicals.
Zeitschrift Online-Publikation |
| Soggetto non controllato | Banking |
| ISSN | 1432-1122 |
| Formato | Materiale a stampa |
| Livello bibliografico | Periodico |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910138886603321 |
| Berlin, : Springer | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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An Introduction to Continuous-Time Stochastic Processes [[electronic resource] ] : Theory, Models, and Applications to Finance, Biology, and Medicine / / by Vincenzo Capasso, David Bakstein
| An Introduction to Continuous-Time Stochastic Processes [[electronic resource] ] : Theory, Models, and Applications to Finance, Biology, and Medicine / / by Vincenzo Capasso, David Bakstein |
| Autore | Capasso Vincenzo <1945-> |
| Edizione | [4th ed. 2021.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2021 |
| Descrizione fisica | 1 online resource (574 pages) |
| Disciplina | 519.2 |
| Collana | Modeling and Simulation in Science, Engineering and Technology |
| Soggetto topico |
Stochastic processes
Stochastic models Mathematical models Social sciences - Mathematics Biomathematics Stochastic Processes Stochastic Modelling Mathematical Modeling and Industrial Mathematics Mathematics in Business, Economics and Finance Mathematical and Computational Biology Processos estocàstics Models matemàtics |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-69653-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Foreword -- Preface to the Fourth Edition -- Preface to the Third Edition -- Preface to the Second Edition -- Preface -- Part I: Theory of Stochastic Processes -- Fundamentals of Probability -- Stochastic Processes -- The Itô Integral -- Stochastic Differential Equations -- Stability, Stationary, Ergodicity -- Part II: Applications of Stochastic Processes -- Applications to Finance and Insurance -- Applications to Biology and Medicine -- Measure and Integration -- Convergence of Probability Measures on Metric Spaces -- Diffusion Approximation of a Langevin System -- Elliptic and Parabolic Equations -- Semigroups of Linear Operators -- Stability of Ordinary Differential Equations -- References -- Nomenclature -- Index. |
| Record Nr. | UNISA-996466403203316 |
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Capasso Vincenzo <1945->
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| Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2021 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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An Introduction to Continuous-Time Stochastic Processes [[electronic resource] ] : Theory, Models, and Applications to Finance, Biology, and Medicine / / by Vincenzo Capasso, David Bakstein
| An Introduction to Continuous-Time Stochastic Processes [[electronic resource] ] : Theory, Models, and Applications to Finance, Biology, and Medicine / / by Vincenzo Capasso, David Bakstein |
| Autore | Capasso Vincenzo <1945-> |
| Edizione | [4th ed. 2021.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2021 |
| Descrizione fisica | 1 online resource (574 pages) |
| Disciplina | 519.2 |
| Collana | Modeling and Simulation in Science, Engineering and Technology |
| Soggetto topico |
Stochastic processes
Stochastic models Mathematical models Social sciences - Mathematics Biomathematics Stochastic Processes Stochastic Modelling Mathematical Modeling and Industrial Mathematics Mathematics in Business, Economics and Finance Mathematical and Computational Biology Processos estocàstics Models matemàtics |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-69653-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Foreword -- Preface to the Fourth Edition -- Preface to the Third Edition -- Preface to the Second Edition -- Preface -- Part I: Theory of Stochastic Processes -- Fundamentals of Probability -- Stochastic Processes -- The Itô Integral -- Stochastic Differential Equations -- Stability, Stationary, Ergodicity -- Part II: Applications of Stochastic Processes -- Applications to Finance and Insurance -- Applications to Biology and Medicine -- Measure and Integration -- Convergence of Probability Measures on Metric Spaces -- Diffusion Approximation of a Langevin System -- Elliptic and Parabolic Equations -- Semigroups of Linear Operators -- Stability of Ordinary Differential Equations -- References -- Nomenclature -- Index. |
| Record Nr. | UNINA-9910485588803321 |
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Capasso Vincenzo <1945->
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| Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2021 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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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 |
| 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 |
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Dolgopyat Dmitry
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| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2023 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Soggetto topico
-
Stochastic Processes
(25)
- Stochastic processes (21)
- Probabilities (11)
- Probability Theory (11)
- Processos estocàstics (6)