Markov Chains And Invariant Probabilities

Author by : Onésimo Hernández-Lerma
Language : en
Publisher by : Birkhäuser
Format Available : PDF, ePub, Mobi
Total Read : 89
Total Download : 207
File Size : 48,7 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).


Markov Chains And Invariant Probabilities

Author by : Onesimo Hernandez-Lerma
Language : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 55
Total Download : 880
File Size : 40,9 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).


Invariant Probabilities Of Markov Feller Operators And Their Supports

Author by : Radu Zaharopol
Language : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 79
Total Download : 466
File Size : 55,7 Mb
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Description : This book covers invariant probabilities for a large class of discrete-time homogeneous Markov processes known as Feller processes. These Feller processes appear in the study of iterated function systems with probabilities, convolution operators, and certain time series. From the reviews: "A very useful reference for researchers wishing to enter the area of stationary Markov processes both from a probabilistic and a dynamical point of view." --MONATSHEFTE FÜR MATHEMATIK


Invariant Probabilities Of Transition Functions

Author by : Radu Zaharopol
Language : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 22
Total Download : 248
File Size : 52,9 Mb
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Description : The structure of the set of all the invariant probabilities and the structure of various types of individual invariant probabilities of a transition function are two topics of significant interest in the theory of transition functions, and are studied in this book. The results obtained are useful in ergodic theory and the theory of dynamical systems, which, in turn, can be applied in various other areas (like number theory). They are illustrated using transition functions defined by flows, semiflows, and one-parameter convolution semigroups of probability measures. In this book, all results on transition probabilities that have been published by the author between 2004 and 2008 are extended to transition functions. The proofs of the results obtained are new. For transition functions that satisfy very general conditions the book describes an ergodic decomposition that provides relevant information on the structure of the corresponding set of invariant probabilities. Ergodic decomposition means a splitting of the state space, where the invariant ergodic probability measures play a significant role. Other topics covered include: characterizations of the supports of various types of invariant probability measures and the use of these to obtain criteria for unique ergodicity, and the proofs of two mean ergodic theorems for a certain type of transition functions. The book will be of interest to mathematicians working in ergodic theory, dynamical systems, or the theory of Markov processes. Biologists, physicists and economists interested in interacting particle systems and rigorous mathematics will also find this book a valuable resource. Parts of it are suitable for advanced graduate courses. Prerequisites are basic notions and results on functional analysis, general topology, measure theory, the Bochner integral and some of its applications.


Markov Chains

Author by : Bruno Sericola
Language : en
Publisher by : John Wiley & Sons
Format Available : PDF, ePub, Mobi
Total Read : 26
Total Download : 201
File Size : 51,5 Mb
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Description : Markov chains are a fundamental class of stochastic processes.They are widely used to solve problems in a large number of domainssuch as operational research, computer science, communicationnetworks and manufacturing systems. The success of Markov chains ismainly due to their simplicity of use, the large number ofavailable theoretical results and the quality of algorithmsdeveloped for the numerical evaluation of many metrics ofinterest. The author presents the theory of both discrete-time andcontinuous-time homogeneous Markov chains. He carefully examinesthe explosion phenomenon, the Kolmogorov equations, the convergenceto equilibrium and the passage time distributions to a state and toa subset of states. These results are applied to birth-and-deathprocesses. He then proposes a detailed study of the uniformizationtechnique by means of Banach algebra. This technique is used forthe transient analysis of several queuing systems. Contents 1. Discrete-Time Markov Chains 2. Continuous-Time Markov Chains 3. Birth-and-Death Processes 4. Uniformization 5. Queues About the Authors Bruno Sericola is a Senior Research Scientist at Inria Rennes– Bretagne Atlantique in France. His main research activityis in performance evaluation of computer and communication systems,dependability analysis of fault-tolerant systems and stochasticmodels.


Markov Chains And Stochastic Stability

Author by : Sean Meyn
Language : en
Publisher by : Cambridge University Press
Format Available : PDF, ePub, Mobi
Total Read : 17
Total Download : 397
File Size : 42,8 Mb
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Description : New up-to-date edition of this influential classic on Markov chains in general state spaces. Proofs are rigorous and concise, the range of applications is broad and knowledgeable, and key ideas are accessible to practitioners with limited mathematical background. New commentary by Sean Meyn, including updated references, reflects developments since 1996.


Markov Chains Theory And Applications

Author by : Dean L. Isaacson
Language : en
Publisher by : John Wiley & Sons
Format Available : PDF, ePub, Mobi
Total Read : 73
Total Download : 657
File Size : 45,9 Mb
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Description : Fundamental concepts of Markov chains; The classical approach to markov chains; The algebraic approach to Markov chains; Nonstationary Markov chains and the ergodic coeficient; Analysis of a markov chain on a computer; Continuous time Markov chains.