Ergodic Behavior Of Markov Processes

Author by : Alexei Kulik
Language : en
Publisher by : Walter de Gruyter GmbH & Co KG
Format Available : PDF, ePub, Mobi
Total Read : 42
Total Download : 695
File Size : 40,8 Mb
pdf pdf

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


The Ergodic Theory Of Markov Processes

Author by : Shaul R. Foguel
Language : en
Publisher by :
Format Available : PDF, ePub, Mobi
Total Read : 56
Total Download : 619
File Size : 50,8 Mb
pdf pdf

Description :


Markov Chains And Invariant Probabilities

Author by : Onesimo Hernandez-Lerma
Language : en
Publisher by : Birkhäuser
Format Available : PDF, ePub, Mobi
Total Read : 45
Total Download : 832
File Size : 42,8 Mb
pdf pdf

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).


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 : 72
Total Download : 704
File Size : 50,6 Mb
pdf pdf

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 : 61
Total Download : 772
File Size : 41,5 Mb
pdf pdf

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 : 34
Total Download : 720
File Size : 40,7 Mb
pdf pdf

Description : The first comprehensive account of controlled diffusions with a focus on ergodic or 'long run average' control.


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 : 42
Total Download : 816
File Size : 52,5 Mb
pdf pdf

Description : This book provides a rigorous but elementary introduction to the theory of Markov Processes on a countable state space. It should be accessible to students with a solid undergraduate background in mathematics, including students from engineering, economics, physics, and biology. Topics covered are: Doeblin's theory, general ergodic properties, and continuous time processes. Applications are dispersed throughout the book. In addition, a whole chapter is devoted to reversible processes and the use of their associated Dirichlet forms to estimate the rate of convergence to equilibrium. These results are then applied to the analysis of the Metropolis (a.k.a simulated annealing) algorithm. The corrected and enlarged 2nd edition contains a new chapter in which the author develops computational methods for Markov chains on a finite state space. Most intriguing is the section with a new technique for computing stationary measures, which is applied to derivations of Wilson's algorithm and Kirchoff's formula for spanning trees in a connected graph.


On The Ergodic Theory Of Markov Operators

Author by : Benton Niles Jamison
Language : en
Publisher by :
Format Available : PDF, ePub, Mobi
Total Read : 48
Total Download : 122
File Size : 54,5 Mb
pdf pdf

Description :


Markov Chains

Author by : D. Revuz
Language : en
Publisher by : Elsevier
Format Available : PDF, ePub, Mobi
Total Read : 88
Total Download : 297
File Size : 46,6 Mb
pdf pdf

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.


Topics In Stochastic Processes

Author by : Robert B. Ash
Language : en
Publisher by : Academic Press
Format Available : PDF, ePub, Mobi
Total Read : 19
Total Download : 353
File Size : 47,9 Mb
pdf pdf

Description : Topics in Stochastic Processes covers specific processes that have a definite physical interpretation and that explicit numerical results can be obtained. This book contains five chapters and begins with the L2 stochastic processes and the concept of prediction theory. The next chapter discusses the principles of ergodic theorem to real analysis, Markov chains, and information theory. Another chapter deals with the sample function behavior of continuous parameter processes. This chapter also explores the general properties of Martingales and Markov processes, as well as the one-dimensional Brownian motion. The aim of this chapter is to illustrate those concepts and constructions that are basic in any discussion of continuous parameter processes, and to provide insights to more advanced material on Markov processes and potential theory. The final chapter demonstrates the use of theory of continuous parameter processes to develop the Itô stochastic integral. This chapter also provides the solution of stochastic differential equations. This book will be of great value to mathematicians, engineers, and physicists.