Taboo Probabilities in Markov Chains with a Discrete Parameter and a Stationary Transition Matrix
Title | Taboo Probabilities in Markov Chains with a Discrete Parameter and a Stationary Transition Matrix PDF eBook |
Author | Travis Ray Aven |
Publisher | |
Pages | 94 |
Release | 1969 |
Genre | |
ISBN |
Markov Chains with Stationary Transition Probabilities
Title | Markov Chains with Stationary Transition Probabilities PDF eBook |
Author | Kai Lai Chung |
Publisher | Springer |
Pages | 287 |
Release | 2013-03-08 |
Genre | Mathematics |
ISBN | 3642496865 |
The theory of Markov chains, although a special case of Markov processes, is here developed for its own sake and presented on its own merits. In general, the hypothesis of a denumerable state space, which is the defining hypothesis of what we call a "chain" here, generates more clear-cut questions and demands more precise and definitive an swers. For example, the principal limit theorem (§§ 1. 6, II. 10), still the object of research for general Markov processes, is here in its neat final form; and the strong Markov property (§ 11. 9) is here always applicable. While probability theory has advanced far enough that a degree of sophistication is needed even in the limited context of this book, it is still possible here to keep the proportion of definitions to theorems relatively low. . From the standpoint of the general theory of stochastic processes, a continuous parameter Markov chain appears to be the first essentially discontinuous process that has been studied in some detail. It is common that the sample functions of such a chain have discontinuities worse than jumps, and these baser discontinuities play a central role in the theory, of which the mystery remains to be completely unraveled. In this connection the basic concepts of separability and measurability, which are usually applied only at an early stage of the discussion to establish a certain smoothness of the sample functions, are here applied constantly as indispensable tools.
Discrete Parameter Markov Chains with Stationary Transition Probabilities
Title | Discrete Parameter Markov Chains with Stationary Transition Probabilities PDF eBook |
Author | Kevin S. Tait |
Publisher | |
Pages | 0 |
Release | 1955 |
Genre | |
ISBN |
An Introduction to Discrete Parameter Markov Chains with Stationary Transition Probabilities
Title | An Introduction to Discrete Parameter Markov Chains with Stationary Transition Probabilities PDF eBook |
Author | Steven Roy Morris |
Publisher | |
Pages | 124 |
Release | 1977 |
Genre | |
ISBN |
Continuous Parameter Markov Chains
Title | Continuous Parameter Markov Chains PDF eBook |
Author | Kai Lai Chung |
Publisher | |
Pages | 30 |
Release | 1958 |
Genre | Markov processes |
ISBN |
Discrete-Time Markov Chains
Title | Discrete-Time Markov Chains PDF eBook |
Author | George Yin |
Publisher | Springer Science & Business Media |
Pages | 372 |
Release | 2005 |
Genre | Business & Economics |
ISBN | 9780387219486 |
Focusing on discrete-time-scale Markov chains, the contents of this book are an outgrowth of some of the authors' recent research. The motivation stems from existing and emerging applications in optimization and control of complex hybrid Markovian systems in manufacturing, wireless communication, and financial engineering. Much effort in this book is devoted to designing system models arising from these applications, analyzing them via analytic and probabilistic techniques, and developing feasible computational algorithms so as to reduce the inherent complexity. This book presents results including asymptotic expansions of probability vectors, structural properties of occupation measures, exponential bounds, aggregation and decomposition and associated limit processes, and interface of discrete-time and continuous-time systems. One of the salient features is that it contains a diverse range of applications on filtering, estimation, control, optimization, and Markov decision processes, and financial engineering. This book will be an important reference for researchers in the areas of applied probability, control theory, operations research, as well as for practitioners who use optimization techniques. Part of the book can also be used in a graduate course of applied probability, stochastic processes, and applications.
Markov Chains
Title | Markov Chains PDF eBook |
Author | David Freedman |
Publisher | Springer Science & Business Media |
Pages | 395 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 1461255007 |
A long time ago I started writing a book about Markov chains, Brownian motion, and diffusion. I soon had two hundred pages of manuscript and my publisher was enthusiastic. Some years and several drafts later, I had a thousand pages of manuscript, and my publisher was less enthusiastic. So we made it a trilogy: Markov Chains Brownian Motion and Diffusion Approximating Countable Markov Chains familiarly - MC, B & D, and ACM. I wrote the first two books for beginning graduate students with some knowledge of probability; if you can follow Sections 10.4 to 10.9 of Markov Chains you're in. The first two books are quite independent of one another, and completely independent of the third. This last book is a monograph which explains one way to think about chains with instantaneous states. The results in it are supposed to be new, except where there are specific disclaim ers; it's written in the framework of Markov Chains. Most of the proofs in the trilogy are new, and I tried hard to make them explicit. The old ones were often elegant, but I seldom saw what made them go. With my own, I can sometimes show you why things work. And, as I will VB1 PREFACE argue in a minute, my demonstrations are easier technically. If I wrote them down well enough, you may come to agree.