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. 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."

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From the reviews of the second edition: "Stopped random walks occur in sequential analysis renewal theory and queueing theory several applications are discussed in the text. ! The book under review is the second edition of a book first published in 1988 ! . lengthy bibliography from the first edition has been brought up to date. ! an excellent reference and its material is still worthy of study." (Thomas Polaski, Mathematical Reviews, Issue 2010 f) "This is definitely a book for the specialist in the field. ! It would suit an academic or a researcher ! seeking to use random walks as a tool for some real-world problem. ! the material is very thorough and there are plentiful references. All results are rigorously established, either by a formal proof or by pointing the reader in the right direction. It will enable any researcher to be right up to date with the latest developments in the field." (F. McGonigal, Journal of the Operational Research Society, Vol. 62 (2), 2011)

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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.

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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.

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