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Exponential Moments of First Passage Times and Related Quantities for Random Walks
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematical Statistics.
2010 (English)In: Electronic Communications in Probability, ISSN 1083-589X, Vol. 15, 365-375 p.Article in journal (Refereed) Published
Abstract [en]

For a zero-delayed random walk on the real line, let tau(x), N(x) and rho(x) denote the first passage time into the interval (x,infinity), the number of visits to the interval (-infinity,x] and the last exit time from (-infinity,x], respectively. In the present paper, we provide ultimate criteria for the finiteness of exponential moments of these quantities. Moreover, whenever these moments are finite, we derive their asymptotic behaviour, as x -> infinity.

Place, publisher, year, edition, pages
2010. Vol. 15, 365-375 p.
Keyword [en]
first-passage time, last exit time, number of visits, random walk, renewal theory
National Category
URN: urn:nbn:se:uu:diva-134550ISI: 000282650000001OAI: oai:DiVA.org:uu-134550DiVA: diva2:372973
Available from: 2010-11-29 Created: 2010-11-29 Last updated: 2011-03-01Bibliographically approved

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