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The ruin problem and cover times of asymmetric random walks and Brownian motions
KTH, Superseded Departments, Mathematics.
2000 (English)In: Advances in Applied Probability, ISSN 0001-8678, E-ISSN 1475-6064, Vol. 32, no 1, 177-192 p.Article in journal (Refereed) Published
Abstract [en]

A simple asymmetric random walk on the integers is stopped when its range is of a given length. When and where is it stopped? Analogous questions can be stated for a Brownian motion. Such problems are studied using results for the classical ruin problem, yielding results for the cover time and the range, both for asymmetric random walks and Brownian motion with drift.

Place, publisher, year, edition, pages
2000. Vol. 32, no 1, 177-192 p.
Keyword [en]
random walk, cover times, Brownian motion, generating functions, Laplace transforms, range, stopping time, first-passage time, Wiener, process, range
URN: urn:nbn:se:kth:diva-19777ISI: 000087187300011OAI: diva2:338469
QC 20100525Available from: 2010-08-10 Created: 2010-08-10Bibliographically approved

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