Large Deviations for Markov Chains

ISBN-13: 9781316511893 / Angielski / Twarda / 2022 / 230 str.

Ohio) de Acos Alejandro D. (Case Western Reserve University

Opis

A study of large deviations for empirical measures and vector-valued additive functionals of general state space Markov chains.

Recenzje

'The theory of large deviations is an important way to understand many mathematical and physical models. This book covers the fascinating topic of large deviations for empirical measures and additive functionals of Markov chains with general state space, a subject on which the author is a leading expert who has made crucial contributions. Markov chains represent a large class of stochastic models with a wide spectrum of behaviors. It is remarkable that any universal results, like the ones given in the book, can be formulated for such a large family. It is equally remarkable that the book develops a sharp link between the large deviations and the degree of recurrence of Markov chains. The book does a superb job of clarification, comparison and identification of the rate functions that govern the large deviations.' Xia Chen, University of Tennessee

Spis treści

Preface; 1. Introduction; 2. Lower bounds and a property of lambda; 3. Upper bounds I; 4. Identification and reconciliation of rate functions; 5. Necessary conditions – bounds on the rate function, invariant measures, irreducibility and recurrence; 6. Upper bounds II – equivalent analytic conditions; 7. Upper bounds III – sufficient conditions; 8. The large deviations principle for empirical measures; 9. The case when S is countable and P is matrix irreducible; 10. Examples; 11. Large deviations for vector-valued additive functionals; Appendix A; Appendix B; Appendix C; Appendix D; Appendix E; Appendix F; Appendix G; Appendix H; Appendix I; Appendix J; Appendix K; References; Author index; Subject index.