Continuous Time Markov Processes : An Introduction (Graduate Studies in Mathematics)

Liggett, Thomas M./ Krantz, Steven G.

American Mathematical Society（2010/08発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 271 p.
• 言語 ENG
• 商品コード 9781470481728

Full Description

Markov processes are among the most important stochastic processes for both theory and applications. This book develops the general theory of these processes and applies this theory to various special examples. The initial chapter is devoted to the most important classical example-one-dimensional Brownian motion. This, together with a chapter on continuous time Markov chains, provides the motivation for the general setup based on semigroups and generators. Chapters on stochastic calculus and probabilistic potential theory give an introduction to some of the key areas of application of Brownian motion and its relatives. A chapter on interacting particle systems treats a more recently developed class of Markov processes that have as their origin problems in physics and biology. This is a textbook for a graduate course that can follow one that covers basic probabilistic limit theorems and discrete time processes.

Contents

Chapters;
Chapter 1. Fundamental concepts;
Chapter 2. Complex line integrals;
Chapter 3. Applications of the Cauchy integral;
Chapter 4. Meromorphic functions and residues;
Chapter 5. The zeros of a holomorphic function;
Chapter 6. Holomorphic functions as geometric mappings;
Chapter 7. Harmonic functions;
Chapter 8. Infinite series and products;
Chapter 9. Applications of infinite sums and products;
Chapter 10. Analytic continuation;
Chapter 11. Topology;
Chapter 12. Rational approximation theory;
Chapter 13. Special classes of holomorphic functions;
Chapter 14. Hilbert spaces of holomorphic functions, the Bergman kernel, and biholomorphic mappings;
Chapter 15. Special functions;
Chapter 16. The prime number theorem; Appendix A. Real analysis; Appendix B. The statement and proof of Goursat's theorem