Stopped Random Walks
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 "noise".
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 "probability theory", "random walks" or "random walks and renewal processes", as well as for self-study.
From the reviews:
"The book provides a nice synthesis of a lot of useful material."
--American Mathematical Society
".[a] clearly written book, useful for researcher and student."
Second edition features a new chapter on perturbed random walks, which are modeled as random walks plus “noise”Presents updates to the first edition, including an outlook on further results, extensions, and generalizations on the subjectClose to 100 additional bibliographic references added to some 200 original onesConcise blend of material useful for both the researcher and student of probability theorySelf-contained text motivated by examples and problemsMay be used in the classroom or for self-study