Markov chains. (Record no. 59987)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 03664nam a22002295i 4500 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 180630s2018 nyu 000 0 eng |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 9783319977034 |
| 041 ## - LANGUAGE CODE | |
| Language code of text/sound track or separate title | eng |
| 080 ## - UNIVERSAL DECIMAL CLASSIFICATION NUMBER | |
| Universal Decimal Classification number | 519.12 |
| Item number | DOU |
| 100 ## - MAIN ENTRY--AUTHOR NAME | |
| Personal name | Douc, Randal |
| 245 00 - TITLE STATEMENT | |
| Title | Markov chains. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Place of publication | Cham |
| Name of publisher | Springer |
| Year of publication | 2018 |
| 300 ## - PHYSICAL DESCRIPTION | |
| Number of Pages | 757 |
| 505 ## - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Part I Foundations.- Markov Chains: Basic Definitions.- Examples of Markov Chains.- Stopping Times and the Strong Markov Property.- Martingales, Harmonic Functions and Polsson-Dirichlet Problems.- Ergodic Theory for Markov Chains.- Part II Irreducible Chains: Basics.- Atomic Chains.- Markov Chains on a Discrete State Space.- Convergence of Atomic Markov Chains.- Small Sets, Irreducibility and Aperiodicity.- Transience, Recurrence and Harris Recurrence.- Splitting Construction and Invariant Measures.- Feller and T-kernels.- Part III Irreducible Chains: Advanced Topics.- Rates of Convergence for Atomic Markov Chains.- Geometric Recurrence and Regularity.- Geometric Rates of Convergence.- (f, r)-recurrence and Regularity.- Subgeometric Rates of Convergence.- Uniform and V-geometric Ergodicity by Operator Methods.- Coupling for Irreducible Kernels.- Part IV Selected Topics.- Convergence in the Wasserstein Distance.- Central Limit Theorems.- Spectral Theory.- Concentration Inequalities.- Appendices.- A Notations.- B Topology, Measure, and Probability.- C Weak Convergence.- D Total and V-total Variation Distances.- E Martingales.- F Mixing Coefficients.- G Solutions to Selected Exercises. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | This book covers the classical theory of Markov chains on general state-spaces as well as many recent developments. The theoretical results are illustrated by simple examples, many of which are taken from Markov Chain Monte Carlo methods. The book is self-contained, while all the results are carefully and concisely proven. Bibliographical notes are added at the end of each chapter to provide an overview of the literature. Part I lays the foundations of the theory of Markov chain on general states-space. Part II covers the basic theory of irreducible Markov chains on general states-space, relying heavily on regeneration techniques. These two parts can serve as a text on general state-space applied Markov chain theory. Although the choice of topics is quite different from what is usually covered, where most of the emphasis is put on countable state space, a graduate student should be able to read almost all these developments without any mathematical background deeper than that needed to study countable state space (very little measure theory is required). Part III covers advanced topics on the theory of irreducible Markov chains. The emphasis is on geometric and subgeometric convergence rates and also on computable bounds. Some results appeared for a first time in a book and others are original. Part IV are selected topics on Markov chains, covering mostly hot recent developments. It represents a biased selection of topics, reflecting the authors own research inclinations. This includes quantitative bounds of convergence in Wasserstein distances, spectral theory of Markov operators, central limit theorems for additive functionals and concentration inequalities. Some of the results in Parts III and IV appear for the first time in book form and some are original |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Distribution (Probability theory) Distribution (Théorie des probabilités) Markov-Kette Probability Theory and Stochastic Processes distribution (statistics-related concept) |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) | |
| Topical term or geographic name as entry element | Mathematics |
| 700 ## - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Eric Moulines, |
| 700 ## - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Pierre Priouret |
| 700 ## - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Philippe Soulier |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | BOOKS |
| Withdrawn status | Lost status | Damaged status | Not for loan | Current library | Shelving location | Full call number | Accession Number | Koha item type |
|---|---|---|---|---|---|---|---|---|
| IMSc Library | First Floor, Rack No: 34, Shelf No: 39 | 519.12 DOU | 77461 | BOOKS |