Markov Processes: Characterization and Convergence (Wiley Series in Probability and Statistics): 623 - Softcover

"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]anyone 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 [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.

The recognition that each method for verifying weak convergence is closely tied to a method for characterizing the limiting process Sparked this broad study of characterization and convergence problems for Markov processes. A number of topics are presented for the first time in book form, such as Martingale problems for general Markov processes, powerful criteria for convergence in distribution in DE[O, ???), multiple random time transformations, duality as a method of characterizing Markov processes, and characterizations of stationary distributions. The authors illustrate several different approaches to proving weak approximation theorems-- operator semigroup convergence theorems, Martingale characterization of Markov processes, and representation of the processes as solutions of stochastic equations. The heart of the book reveals the main characterization and convergence results, with an emphasis on diffusion processes. Applications to branching and population processes, genetic models, and random evolutions, are given. Useful to the professional as a reference, 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.