Markov Chains And Invariant Probabilities

Author by : Onésimo Hernández-Lerma
Language : en
Publisher by : Birkhäuser
Format Available : PDF, ePub, Mobi
Total Read : 47
Total Download : 617
File Size : 45,7 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 : 79
Total Download : 133
File Size : 41,5 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 Stochastic Stability

Author by : Sean Meyn
Language : en
Publisher by : Cambridge University Press
Format Available : PDF, ePub, Mobi
Total Read : 98
Total Download : 377
File Size : 51,9 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 : ja
Publisher by : John Wiley & Sons
Format Available : PDF, ePub, Mobi
Total Read : 16
Total Download : 881
File Size : 41,8 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.


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 : 55
Total Download : 775
File Size : 47,8 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


Markov Chains

Author by : D. Revuz
Language : en
Publisher by : Elsevier
Format Available : PDF, ePub, Mobi
Total Read : 98
Total Download : 277
File Size : 48,5 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.


Markov Chains

Author by : Bruno Sericola
Language : en
Publisher by : John Wiley & Sons
Format Available : PDF, ePub, Mobi
Total Read : 33
Total Download : 910
File Size : 47,6 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

Author by : J. R. Norris
Language : en
Publisher by : Cambridge University Press
Format Available : PDF, ePub, Mobi
Total Read : 52
Total Download : 547
File Size : 52,8 Mb
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Description : Markov chains are central to the understanding of random processes. This is not only because they pervade the applications of random processes, but also because one can calculate explicitly many quantities of interest. This textbook, aimed at advanced undergraduate or MSc students with some background in basic probability theory, focuses on Markov chains and quickly develops a coherent and rigorous theory whilst showing also how actually to apply it. Both discrete-time and continuous-time chains are studied. A distinguishing feature is an introduction to more advanced topics such as martingales and potentials in the established context of Markov chains. There are applications to simulation, economics, optimal control, genetics, queues and many other topics, and exercises and examples drawn both from theory and practice. It will therefore be an ideal text either for elementary courses on random processes or those that are more oriented towards applications.