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Stopped random walks. Limit theorems and applications. 2nd ed. (English) Zbl 1166.60001
Springer Series in Operations Research and Financial Engineering. New York, NY: Springer (ISBN 978-0-387-87834-8/hbk; 978-0-387-87835-5/ebook). xiii, 263 p. (2009).
This is an updated second edition of the book [A. Gut, Stopped random walks. Limit theorems and applications. Applied Probability, Vol. 5. (New York) etc.: Springer-Verlag. (1988; Zbl 0634.60061)]. The present edition contains a new Chapter 6 devoted to the perturbed random walks, that is processes of the type \(Z_n=S_n+\xi_n\), where \(S_n\) is a random walk with positive finite mean increments, and \(\xi_n\) is a perturbation sequence satisfying \(n^{-1}\xi_n\to 0\) a.s. Various limit theorems are proven in this chapter, in particular for the case \(Z_n=n g(\frac{1}{n}\sum_{k=1}^n Y_k)\), with \(Y_k\) being i.i.d. random variables with positive finite mean, and \(g(\cdot)\) belonging to a certain class of non-negative continuous functions. The book’s bibliography is also considerably extended and contains 324 entries.

60-02 Research exposition (monographs, survey articles) pertaining to probability theory
60G50 Sums of independent random variables; random walks
60Fxx Limit theorems in probability theory
60K05 Renewal theory
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