Markov Processes: Characterization and Convergence

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John Wiley & Sons, Sep 25, 2009 - Mathematics - 552 pages
The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists.

"[A]nyone who works with Markov processes whose state space is uncountably infinite will need this most impressive book as a guide and reference."
-American Scientist

"There is no question but that space should immediately be reserved for [this] book on the library shelf. Those who aspire to mastery of the contents should also reserve a large number of long winter evenings."
-Zentralblatt für Mathematik und ihre Grenzgebiete/Mathematics Abstracts

"Ethier and Kurtz have produced an excellent treatment of the modern theory of Markov processes that [is] useful both as a reference work and as a graduate textbook."
-Journal of Statistical Physics

Markov Processes presents several different approaches to proving weak approximation theorems for Markov processes, emphasizing the interplay of methods of characterization and approximation. Martingale problems for general Markov processes are systematically developed for the first time in book form. Useful to the professional as a reference and suitable for the graduate student as a text, this volume features a table of the interdependencies among the theorems, an extensive bibliography, and end-of-chapter problems.
 

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Contents

Introduction
1
1 Operator Semigroups
6
2 Stochastic Processes and Martingales
49
3 Convergence of Probability Measures
95
4 Generators and Markov Processes
155
5 Stochastic Integral Equations
275
6 Random Time Changes
306
7 Invariance Principles and Diffusion Approximations
337
9 Branching Processes
386
10 Genetic Models
410
11 Density Dependent Population Processes
452
12 Random Evolutions
468
Appendixes
492
References
508
Index
521
Flowchart
529

8 Examples of Generators
365

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About the author (2009)

STEWART N. ETHIER, PhD, is Professor of Mathematics at the University of Utah. He received his PhD in mathematics at the University of Wisconsin–Madison.

THOMAS G. KURTZ, PhD, is Professor of Mathematics and Statistics at the University of Wisconsin–Madison. He is a Book Review Editor for The Annals of Probability and the author of Approximation of Population Processes. Dr. Kurtz obtained his PhD in mathematics at Stanford University.

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