Overview
- 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
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Series in Operations Research and Financial Engineering (ORFE)
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Table of contents (6 chapters)
Keywords
About this book
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, queueing theory, storage and inventory theory, insurance risk theory, reliability theory, and the theory of counters. 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, 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”.
Reviews
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)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Stopped Random Walks
Book Subtitle: Limit Theorems and Applications
Authors: Allan Gut
Series Title: Springer Series in Operations Research and Financial Engineering
DOI: https://doi.org/10.1007/978-0-387-87835-5
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag New York 2009
Hardcover ISBN: 978-0-387-87834-8Published: 27 February 2009
Softcover ISBN: 978-1-4419-2773-6Published: 15 December 2010
eBook ISBN: 978-0-387-87835-5Published: 03 April 2009
Series ISSN: 1431-8598
Series E-ISSN: 2197-1773
Edition Number: 2
Number of Pages: XIV, 263
Additional Information: Originally published as volume 5 in the series: Applied Probability
Topics: Probability Theory and Stochastic Processes, Operations Research, Management Science
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