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Local Limit Theorems for Inhomogeneous Markov Chains
This book introduces a new general theory of local limit theorems for additive functionals of Markov chains, covering local, moderate, and large deviations. The local central limit theorem is extended to Markov chains where the state spaces and transition probabilities can change over time, used for modeling Markovian systems dependent on external time-dependent parameters. The book also provides nearly optimal conditions for 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 appendices with background material, numerous examples, and an account of the historical background of the subject makes this self-contained book accessible to graduate students. It will also be useful for researchers in probability and ergodic theory interested in asymptotic behaviors, Markov chains in random environments, random dynamical systems, and non-stationary systems.
product information:
| Attribute | Value |
|---|---|
| publisher | Springer; 1st ed. 2023 edition (August 1, 2023) |
| language | English |
| paperback | 356 pages |
| isbn_10 | 3031326008 |
| isbn_13 | 978-3031326004 |
| item_weight | 1.1 pounds |
| dimensions | 6.1 x 0.81 x 9.25 inches |
