Stopped Random Walks e-bog

Classical probability theory provides information about random walks after a fixed number of steps. For applications, however, it is more natural to consider random walks evaluated after a random number of steps. Stopped Random Walks: Limit Theorems and Applications shows how this theory can be used to prove limit theorems for renewal counting processes, first passage time processes, and certain two-dimensional random walks, as well as how these results may be used in a variety of applications.The present second edition offers updated content and an outlook on further results, extensions and generalizations. A new chapter introduces nonlinear renewal processes and the theory of perturbed random walks, which are modeled as random walks plus "e;noise"e;.This self-contained research monograph is motivated by numerous examples and problems. With its concise blend of material and over 300 bibliographic references, the book provides a unified and fairly complete treatment of the area. The book may be used in the classroom as part of a course on "e;probability theory"e;, "e;random walks"e; or "e;random walks and renewal processes"e;, as well as for self-study. From the reviews:"e;The book provides a nice synthesis of a lot of useful material."e;--American Mathematical Society"e;...[a] clearly written book, useful for researcher and student."e; --Zentralblatt MATH