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Two-boundary problems for a random walk

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Ukrainian Mathematical Journal Aims and scope

Abstract

We solve main two-boundary problems for a random walk. The generating function of the joint distribution of the first exit time of a random walk from an interval and the value of the overshoot of the random walk over the boundary at exit time is determined. We also determine the generating function of the joint distribution of the first entrance time of a random walk to an interval and the value of the random walk at this time. The distributions of the supremum, infimum, and value of a random walk and the number of upward and downward crossings of an interval by a random walk are determined on a geometrically distributed time interval. We give examples of application of obtained results to a random walk with one-sided exponentially distributed jumps.

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev, Ukraine

    I. I. Ezhov, V. F. Kadankov & T. V. Kadankova

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  1. I. I. Ezhov
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  2. V. F. Kadankov
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  3. T. V. Kadankova
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 11, pp. 1485–1509, November, 2007.

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Ezhov, I.I., Kadankov, V.F. & Kadankova, T.V. Two-boundary problems for a random walk. Ukr Math J 59, 1668–1692 (2007). https://doi.org/10.1007/s11253-008-0018-7

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