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