Stopped random walks: limit theorems and applications

Allan Gut (auth.)9780387878348, 0387878343, 9780387878355

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.”

–Zentralblatt MATH

Table of contents :
Front Matter….Pages i-xxii
Limit Theorems for Stopped Random Walks….Pages 9-47
Renewal Processes and Random Walks….Pages 49-77
Renewal Theory for Random Walks with Positive Drift….Pages 79-113
Generalizations and Extensions….Pages 115-156
Functional Limit Theorems….Pages 157-174
Perturbed Random Walks….Pages 175-221
Back Matter….Pages 223-263