Two-boundary problems for a random walk

I.i. Ezhov, Tetyana Kadankova, Victor Kadankov

Research output: Contribution to journalArticle

6 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)1485-1509
Number of pages24
JournalUkrainian Mathematical Journal
Volume59
Publication statusPublished - 2007

Keywords

  • wo-boundary problems
  • random walk

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