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Mathematics - Probability Theory and Stochastic Processes | Stopped Random Walks - Limit Theorems and Applications

Stopped Random Walks

Limit Theorems and Applications

Gut, Allan

Originally published as volume 5 in the series: Applied Probability

2nd ed. 2009, XIV, 263p.

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  • 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
  • Adds close to 100 bibliographic references onto the approximately 200 original ones
  • Presents a 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

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

Content Level » Graduate

Keywords » Probability theory - Sage - limit theorems - perturbed random walks - probability - renewal processes - two-dimensional random walks

Related subjects » Applications - Probability Theory and Stochastic Processes

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