Format:
1 Online-Ressource
ISBN:
9783031326011
Series Statement:
Lecture Notes in Mathematics 2331
Content:
This book extends the local central limit theorem to inhomogeneous Markov chains whose state spaces and transition probabilities are allowed to change in time. Such chains are used to model Markovian systems depending on external time-dependent parameters. It develops a new general theory of local limit theorems for additive functionals of Markov chains, in the regimes of local, moderate, and large deviations, and provides nearly optimal conditions for the classical expansions, as well as asymptotic corrections when these conditions fail. Applications include local limit theorems for independent but not identically distributed random variables, Markov chains in random environments, and time-dependent perturbations of homogeneous Markov chains. The inclusion of numerous examples, a comprehensive review of the literature, and an account of the historical background of the subject make this self-contained book accessible to graduate students. It will also be useful for researchers in probability and ergodic theory who are interested in asymptotic behaviors, random walks in random environments, random dynamical systems and non-stationary systems.
Additional Edition:
ISBN 9783031326004
Additional Edition:
ISBN 9783031326028
Additional Edition:
Erscheint auch als Druck-Ausgabe Dolgopyat, Dmitry, 1972 - Local limit theorems for inhomogeneous Markov chains Cham : Springer, 2023 ISBN 3031326008
Additional Edition:
ISBN 9783031326004
Language:
English
Keywords:
Markov-Kette
;
Zeitabhängige Zufallsvariable
;
Lokaler Grenzwertsatz
;
Additives Funktional
;
Große Abweichung
;
Zufälliges dynamisches System
;
Nichtstationärer Prozess
DOI:
10.1007/978-3-031-32601-1
