Markov Processes Characterization and Convergence

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 D E [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.Ethier, Stewart N. is the author of 'Markov Processes Characterization and Convergence' with ISBN 9780471081869 and ISBN 0471081868.