Stopped Random Walks (eBook)

Limit Theorems and Applications

Allan Gut (Autor)

eBook Download: PDF

2009 | 2nd ed. 2009
XIV, 263 Seiten
Springer New York (Verlag)
978-0-387-87835-5 (ISBN)

Infos

This new edition offers updated content and an outlook on further results, extensions and generalizations on stopped random walks. It also contains a new chapter on perturbed random walks and nearly 100 new bibliographic references.

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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

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.

Inhalt

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.

Produkt-Details

• Erscheint lt. Verlag: 3.4.2009
• Reihe/Serie: Springer Series in Operations Research and Financial Engineering
• Verlagsort: New York
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Technik
• Schlagworte: limit theorems • perturbed random walks • Probability • Probability Theory • Renewal processes • Sage • two-dimensional random walks
• ISBN-10: 0-387-87835-1 / 0387878351
• ISBN-13: 978-0-387-87835-5 / 9780387878355