Über den Autor
Dr. Allan Gut is a professor of mathematical statistics at Uppsala University in Sweden. He has published many numerous articles, and has authored and co-authored six books, four of which were published by Springer. Three of those books, including the first edition of this book, have sold out, and Probability: A Graduate Course, published in 2005, is selling well.
Preface.- Notations and Symbols.- Introduction.- Limit Theorems for Stopped Random Walks.- Renewal Processes and Random Walks.- Renewal Theory for Random Walks with Positive Drift.- Generalizations and Extensions.- Functional Limit Theorems.- Perturbed Random Walks.- Appendix A: Some Facts from Probability Theory.- Appendix B: Some Facts about Regularly Varying Functions.- Bibliography.- Index.
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. Examples are sequential analysis, queuing theory, storage and inventory theory, insurance risk theory, reliability theory, and the theory of contours. 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-dimenstional random walks, and to how these results are useful in various applications.
This second edition offers updated content and an outlook on further results, extensions and generalizations. A new chapter examines nonlinear renewal processes in order to present the analagous theory for perturbed random walks, modeled as a random walk plus "noise."
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 subject
Close to 100 additional bibliographic references added to some 200 original ones
Concise blend of material useful for both the researcher and student of probability theory
Self-contained text motivated by examples and problems
May be used in the classroom or for self-study