Ergodic Behavior Of Markov Processes

Author by : Alexei Kulik
Language : en
Publisher by : Walter de Gruyter GmbH & Co KG
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Description : The general topic of this book is the ergodic behavior of Markov processes. A detailed introduction to methods for proving ergodicity and upper bounds for ergodic rates is presented in the first part of the book, with the focus put on weak ergodic rates, typical for Markov systems with complicated structure. The second part is devoted to the application of these methods to limit theorems for functionals of Markov processes. The book is aimed at a wide audience with a background in probability and measure theory. Some knowledge of stochastic processes and stochastic differential equations helps in a deeper understanding of specific examples. Contents Part I: Ergodic Rates for Markov Chains and Processes Markov Chains with Discrete State Spaces General Markov Chains: Ergodicity in Total Variation MarkovProcesseswithContinuousTime Weak Ergodic Rates Part II: Limit Theorems The Law of Large Numbers and the Central Limit Theorem Functional Limit Theorems


Eigenvalues Inequalities And Ergodic Theory

Author by : Mu-Fa Chen
Language : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 32
Total Download : 839
File Size : 42,9 Mb
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Description : The first and only book to make this research available in the West Concise and accessible: proofs and other technical matters are kept to a minimum to help the non-specialist Each chapter is self-contained to make the book easy-to-use


Introduction To Ergodic Rates For Markov Chains And Processes

Author by : Kulik, Alexei
Language : en
Publisher by : Universitätsverlag Potsdam
Format Available : PDF, ePub, Mobi
Total Read : 16
Total Download : 996
File Size : 43,6 Mb
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Description : The present lecture notes aim for an introduction to the ergodic behaviour of Markov Processes and addresses graduate students, post-graduate students and interested readers. Different tools and methods for the study of upper bounds on uniform and weak ergodic rates of Markov Processes are introduced. These techniques are then applied to study limit theorems for functionals of Markov processes. This lecture course originates in two mini courses held at University of Potsdam, Technical University of Berlin and Humboldt University in spring 2013 and Ritsumameikan University in summer 2013. Alexei Kulik, Doctor of Sciences, is a Leading researcher at the Institute of Mathematics of Ukrainian National Academy of Sciences.


Ergodic Control Of Diffusion Processes

Author by : Ari Arapostathis
Language : en
Publisher by : Cambridge University Press
Format Available : PDF, ePub, Mobi
Total Read : 82
Total Download : 600
File Size : 42,7 Mb
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Description : The first comprehensive account of controlled diffusions with a focus on ergodic or 'long run average' control.


Markov Chains

Author by : D. Revuz
Language : en
Publisher by : Elsevier
Format Available : PDF, ePub, Mobi
Total Read : 94
Total Download : 769
File Size : 43,6 Mb
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Description : This is the revised and augmented edition of a now classic book which is an introduction to sub-Markovian kernels on general measurable spaces and their associated homogeneous Markov chains. The first part, an expository text on the foundations of the subject, is intended for post-graduate students. A study of potential theory, the basic classification of chains according to their asymptotic behaviour and the celebrated Chacon-Ornstein theorem are examined in detail. The second part of the book is at a more advanced level and includes a treatment of random walks on general locally compact abelian groups. Further chapters develop renewal theory, an introduction to Martin boundary and the study of chains recurrent in the Harris sense. Finally, the last chapter deals with the construction of chains starting from a kernel satisfying some kind of maximum principle.


Studies In Probability And Ergodic Theory

Author by : Gian-Carlo Rota
Language : en
Publisher by :
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Total Read : 87
Total Download : 852
File Size : 46,8 Mb
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Description : Coupling methods for markov processes; On fluctuations of sums of random variables; Almost-sure invariance principle for branching brownian motion; On operator inequalities and projections; Boundary behavior of laplace-stieltjes transforms with applications to uniformly distributed sequences; Regularities of distribution; Strong liftings on topological measured spaces; Mixing transformations in an infinite measure space; On eventually weakly wandering sequences; Gap sequences and eventually weakly wandering sequences; The breakdown of automorphisms of compact topological groups; On the polynomial uniformity of translations on the n-torus; Generalized torus automorphisms are bernoullian; The isomorphism theorem for generalized Bernoulli Schemes; Measurabletransformations on homogeneous spaces; Ergodic transformations of lebesgue spaces.


An Introduction To Markov Processes

Author by : Daniel W. Stroock
Language : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 62
Total Download : 485
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Description : Provides a more accessible introduction than other books on Markov processes by emphasizing the structure of the subject and avoiding sophisticated measure theory Leads the reader to a rigorous understanding of basic theory


Stochastic Networks And Queues

Author by : Philippe Robert
Language : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 83
Total Download : 101
File Size : 48,7 Mb
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Description : Queues and stochastic networks are analyzed in this book with purely probabilistic methods. The purpose of these lectures is to show that general results from Markov processes, martingales or ergodic theory can be used directly to study the corresponding stochastic processes. Recent developments have shown that, instead of having ad-hoc methods, a better understanding of fundamental results on stochastic processes is crucial to study the complex behavior of stochastic networks. In this book, various aspects of these stochastic models are investigated in depth in an elementary way: Existence of equilibrium, characterization of stationary regimes, transient behaviors (rare events, hitting times) and critical regimes, etc. A simple presentation of stationary point processes and Palm measures is given. Scaling methods and functional limit theorems are a major theme of this book. In particular, a complete chapter is devoted to fluid limits of Markov processes.


Markov Chains And Invariant Probabilities

Author by : Onésimo Hernández-Lerma
Language : en
Publisher by : Birkhäuser
Format Available : PDF, ePub, Mobi
Total Read : 13
Total Download : 476
File Size : 55,9 Mb
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Description : This book is about discrete-time, time-homogeneous, Markov chains (Mes) and their ergodic behavior. To this end, most of the material is in fact about stable Mes, by which we mean Mes that admit an invariant probability measure. To state this more precisely and give an overview of the questions we shall be dealing with, we will first introduce some notation and terminology. Let (X,B) be a measurable space, and consider a X-valued Markov chain ~. = {~k' k = 0, 1, ... } with transition probability function (t.pJ.) P(x, B), i.e., P(x, B) := Prob (~k+1 E B I ~k = x) for each x E X, B E B, and k = 0,1, .... The Me ~. is said to be stable if there exists a probability measure (p.m.) /.l on B such that (*) VB EB. /.l(B) = Ix /.l(dx) P(x, B) If (*) holds then /.l is called an invariant p.m. for the Me ~. (or the t.p.f. P).


Convergence In Ergodic Theory And Probability

Author by : Vitaly Bergelson
Language : en
Publisher by : Walter de Gruyter
Format Available : PDF, ePub, Mobi
Total Read : 44
Total Download : 623
File Size : 42,9 Mb
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Description : This series is devoted to the publication of monographs, lecture resp. seminar notes, and other materials arising from programs of the OSU Mathemaical Research Institute. This includes proceedings of conferences or workshops held at the Institute, and other mathematical writings.