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On the sojourn time of a random walk in a strip

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Abstract

We obtain asymptotic representations for the triple transforms of the joint distribution of the sojourn time of a random walk in a strip (as well as in a half-plane) in n steps and of the location at time n under the condition of unboundedly moving-off boundaries of the sets. The Cramér type conditions are imposed on the distribution of jumps.

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Correspondence to V. I. Lotov.

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Original Russian Text Copyright © 2010 Lotov V. I.

The author was supported in part by the Russian Foundation for Basic Research (Grant 09-01-12131).

Novosibirsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 51, No. 4, pp. 785–804, July–August, 2010.

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Lotov, V.I. On the sojourn time of a random walk in a strip. Sib Math J 51, 621–638 (2010). https://doi.org/10.1007/s11202-010-0064-x

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  • DOI: https://doi.org/10.1007/s11202-010-0064-x

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