Markov Processes: Characterization and Convergence By Stewart N. Ethier, Thomas G. Kurtz(auth.)
2005 | 550 Pages | ISBN: 0471081868 | PDF | 13 MB
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 fur Mathematik und ihre Grenzgebiete/Mathematics Abstracts "Ethier and Kurtz have produced an excellent treatment of the modern theory of Markov processes that s 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. Content: Chapter 1 Operator Semigroups (pages 6-48): Chapter 2 Stochastic Processes and Martingales (pages 49-94): Chapter 3 Convergence of Probability Measures (pages 95-154): Chapter 4 Generators and Markov Processes (pages 155-274): Chapter 5 Stochastic Integral Equations (pages 275-305): Chapter 6 Random Time Changes (pages 306-336): Chapter 7 Invariance Principles and Diffusion Approximations (pages 337-364): Chapter 8 Examples of Generators (pages 365-385): Chapter 9 Branching Processes (pages 386-409): Chapter 10 Genetic Models (pages 410-451): Chapter 11 Density Dependent Population Processes (pages 452-467): Chapter 12 Random Evolutions (pages 468-491):