Large Deviations for Additive Functionals of Markov Chains

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Publisher : American Mathematical Soc.
ISBN 13 : 0821890891
Total Pages : 120 pages
Book Rating : 4.99/5 ( download)

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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 and published by American Mathematical Soc.. This book was released on 2014-03-05 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Large Deviations for Markov Chains

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Publisher :
ISBN 13 : 1009063359
Total Pages : 264 pages
Book Rating : 4.57/5 ( download)

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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 and published by . This book was released on 2022-10-12 with total page 264 pages. 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.

Large Deviations for Additive Functionals of Markov Exhangeable Sequences

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ISBN 13 :
Total Pages : 194 pages
Book Rating : 4.63/5 ( download)

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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 and published by . This book was released on 1993 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Local Limit Theorems for Inhomogeneous Markov Chains

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Publisher : Springer Nature
ISBN 13 : 3031326016
Total Pages : 348 pages
Book Rating : 4.11/5 ( download)

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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 and published by Springer Nature. This book was released on 2023-07-31 with total page 348 pages. 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.

Large Deviations for Stochastic Processes

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Publisher : American Mathematical Soc.
ISBN 13 : 1470418703
Total Pages : 426 pages
Book Rating : 4.00/5 ( download)

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Book Synopsis Large Deviations for Stochastic Processes by : Jin Feng

Download or read book Large Deviations for Stochastic Processes written by Jin Feng and published by American Mathematical Soc.. This book was released on 2015-02-03 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the results on large deviations for a class of stochastic processes. Following an introduction and overview, the material is presented in three parts. Part 1 gives necessary and sufficient conditions for exponential tightness that are analogous to conditions for tightness in the theory of weak convergence. Part 2 focuses on Markov processes in metric spaces. For a sequence of such processes, convergence of Fleming's logarithmically transformed nonlinear semigroups is shown to imply the large deviation principle in a manner analogous to the use of convergence of linear semigroups in weak convergence. Viscosity solution methods provide applicable conditions for the necessary convergence. Part 3 discusses methods for verifying the comparison principle for viscosity solutions and applies the general theory to obtain a variety of new and known results on large deviations for Markov processes. In examples concerning infinite dimensional state spaces, new comparison principles are derived for a class of Hamilton-Jacobi equations in Hilbert spaces and in spaces of probability measures.

On the Large Deviation Functions of Markov Chains

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Publisher :
ISBN 13 :
Total Pages : 20 pages
Book Rating : 4.75/5 ( download)

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Book Synopsis On the Large Deviation Functions of Markov Chains by : University of Minnesota. Institute for Mathematics and Its Applications

Download or read book On the Large Deviation Functions of Markov Chains written by University of Minnesota. Institute for Mathematics and Its Applications and published by . This book was released on 1985 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Limit Theorems on Large Deviations for Markov Stochastic Processes

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Publisher : Springer Science & Business Media
ISBN 13 : 9400918526
Total Pages : 192 pages
Book Rating : 4.28/5 ( download)

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Book Synopsis Limit Theorems on Large Deviations for Markov Stochastic Processes by : A.D. Wentzell

Download or read book Limit Theorems on Large Deviations for Markov Stochastic Processes written by A.D. Wentzell and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent decades a new branch of probability theory has been developing intensively, namely, limit theorems for stochastic processes. As compared to classical limit theorems for sums of independent random variables, the generalizations are going here in two directions simultaneously. First, instead of sums of independent variables one considers stochastic processes belonging to certain broad classes. Secondly, instead of the distribution of a single sum - the distribution of the value of a stochastic process at one (time) point - or the joint distribution of the values of a process at a finite number of points, one considers distributions in an infinite-dimensional function space. For stochastic processes constructed, starting from sums of independent random variables, this is the same as considering the joint distribution of an unboundedly increasing number of sums.

Large Deviations Techniques and Applications

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Publisher : Springer Science & Business Media
ISBN 13 : 3642033113
Total Pages : 409 pages
Book Rating : 4.17/5 ( download)

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Book Synopsis Large Deviations Techniques and Applications by : Amir Dembo

Download or read book Large Deviations Techniques and Applications written by Amir Dembo and published by Springer Science & Business Media. This book was released on 2009-11-03 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: Large deviation estimates have proved to be the crucial tool required to handle many questions in statistics, engineering, statistial mechanics, and applied probability. Amir Dembo and Ofer Zeitouni, two of the leading researchers in the field, provide an introduction to the theory of large deviations and applications at a level suitable for graduate students. The mathematics is rigorous and the applications come from a wide range of areas, including electrical engineering and DNA sequences. The second edition, printed in 1998, included new material on concentration inequalities and the metric and weak convergence approaches to large deviations. General statements and applications were sharpened, new exercises added, and the bibliography updated. The present soft cover edition is a corrected printing of the 1998 edition.

Limit Theorems for Functionals of Ergodic Markov Chains with General State Space

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Publisher : American Mathematical Soc.
ISBN 13 : 082181060X
Total Pages : 225 pages
Book Rating : 4.06/5 ( download)

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Book Synopsis Limit Theorems for Functionals of Ergodic Markov Chains with General State Space by : Xia Chen

Download or read book Limit Theorems for Functionals of Ergodic Markov Chains with General State Space written by Xia Chen and published by American Mathematical Soc.. This book was released on 1999 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for graduate students and research mathematicians working probability theory and statistics.

Applied Probability and Queues

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Publisher : Springer Science & Business Media
ISBN 13 : 0387215255
Total Pages : 451 pages
Book Rating : 4.59/5 ( download)

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Book Synopsis Applied Probability and Queues by : Soeren Asmussen

Download or read book Applied Probability and Queues written by Soeren Asmussen and published by Springer Science & Business Media. This book was released on 2008-01-08 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is a highly recommendable survey of mathematical tools and results in applied probability with special emphasis on queueing theory....The second edition at hand is a thoroughly updated and considerably expended version of the first edition.... This book and the way the various topics are balanced are a welcome addition to the literature. It is an indispensable source of information for both advanced graduate students and researchers." --MATHEMATICAL REVIEWS