Markov Chains by Kai Lai Chung

Markov Chains by Kai Lai Chung

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, I. 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.

Kai Lai Chung is an Emeritus Professor of Probability Theory at Stanford University, where he has taught for the past 30 years.

SKU	Unavailable
ISBN 13	9783642620171
ISBN 10	3642620175
Title	Markov Chains
Author	Kai Lai Chung
Series	Grundlehren Der Mathematischen Wissenschaften
Condition	Unavailable
Binding Type	Paperback
Publisher	Springer
Year published	2012-07-17
Number of pages	301
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.