Stopped Random Walks Limit Theorems and Applications /

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...

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Bibliographic Details
Main Author: Gut, Allan. (Author)
Corporate Author: SpringerLink (Online service)
Format: Electronic
Language:English
Published: New York, NY : Springer New York, 2009.
Series:Springer Series in Operations Research and Financial Engineering,
Subjects:
Online Access:https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-0-387-87835-5
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505 0 # |a 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. 
520 # # |a 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 
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