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Author : Alejandro D. de Acosta
Release : 2014-03-05
Genre : Mathematics
Kind : eBook
Book Rating : 891/5 ( reviews)
Book Synopsis Large Deviations for Additive Functionals of Markov Chains by : Alejandro D. de Acosta
Download or read book Large Deviations for Additive Functionals of Markov Chains written by Alejandro D. de Acosta. This book was released on 2014-03-05. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Alejandro D. de Acosta
Release : 2022-10-12
Genre : Mathematics
Kind : eBook
Book Rating : 359/5 ( reviews)
Book Synopsis Large Deviations for Markov Chains by : Alejandro D. de Acosta
Download or read book Large Deviations for Markov Chains written by Alejandro D. de Acosta. This book was released on 2022-10-12. Available in PDF, EPUB and Kindle. Book excerpt: This book studies the large deviations for empirical measures and vector-valued additive functionals of Markov chains with general state space. Under suitable recurrence conditions, the ergodic theorem for additive functionals of a Markov chain asserts the almost sure convergence of the averages of a real or vector-valued function of the chain to the mean of the function with respect to the invariant distribution. In the case of empirical measures, the ergodic theorem states the almost sure convergence in a suitable sense to the invariant distribution. The large deviation theorems provide precise asymptotic estimates at logarithmic level of the probabilities of deviating from the preponderant behavior asserted by the ergodic theorems.
Author : Grant Izmirlian
Release : 1993
Genre :
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Large Deviations for Additive Functionals of Markov Exhangeable Sequences by : Grant Izmirlian
Download or read book Large Deviations for Additive Functionals of Markov Exhangeable Sequences written by Grant Izmirlian. This book was released on 1993. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Dmitry Dolgopyat
Release : 2023-07-31
Genre : Mathematics
Kind : eBook
Book Rating : 016/5 ( reviews)
Book Synopsis Local Limit Theorems for Inhomogeneous Markov Chains by : Dmitry Dolgopyat
Download or read book Local Limit Theorems for Inhomogeneous Markov Chains written by Dmitry Dolgopyat. This book was released on 2023-07-31. Available in PDF, EPUB and Kindle. Book excerpt: This book extends the local central limit theorem to 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. The book 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 appendices with background material, numerous examples, 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, Markov chains in random environments, random dynamical systems and non-stationary systems.
Author : S. R. S. Varadhan
Release : 2016-12-08
Genre : Mathematics
Kind : eBook
Book Rating : 86X/5 ( reviews)
Book Synopsis Large Deviations by : S. R. S. Varadhan
Download or read book Large Deviations written by S. R. S. Varadhan. This book was released on 2016-12-08. Available in PDF, EPUB and Kindle. Book excerpt: The theory of large deviations deals with rates at which probabilities of certain events decay as a natural parameter in the problem varies. This book, which is based on a graduate course on large deviations at the Courant Institute, focuses on three concrete sets of examples: (i) diffusions with small noise and the exit problem, (ii) large time behavior of Markov processes and their connection to the Feynman-Kac formula and the related large deviation behavior of the number of distinct sites visited by a random walk, and (iii) interacting particle systems, their scaling limits, and large deviations from their expected limits. For the most part the examples are worked out in detail, and in the process the subject of large deviations is developed. The book will give the reader a flavor of how large deviation theory can help in problems that are not posed directly in terms of large deviations. The reader is assumed to have some familiarity with probability, Markov processes, and interacting particle systems.
