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‘[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.
Table of Content
Introduction.
1. Operator Semigroups.
2. Stochastic Processes and Martingales.
3. Convergence of Probability Measures.
4. Generators and Markov Processes.
5. Stochastic Integral Equations.
6. Random Time Changes.
7. Invariance Principles and Diffusion Approximations.
8. Examples of Generators.
9. Branching Processes.
10. Genetic Models.
11. Density Dependent Population Processes.
12. Random Evolutions.
Appendixes.
References.
Index.
Flowchart.
About the author
STEWART N. ETHIER, Ph D, is Professor of Mathematics at the
University of Utah. He received his Ph D in mathematics at the
University of Wisconsin-Madison.
THOMAS G. KURTZ, Ph D, 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 Ph D
in mathematics at Stanford University.
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