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Sbornik: Mathematics, 2003, Volume 194, Issue 6, Pages 927–939
DOI: https://doi.org/10.1070/SM2003v194n06ABEH000746 (Mi sm746) 		 
This article is cited in 7 scientific papers (total in 7 papers)

On the number of crossings of a strip by sample paths of a random walk

V. I. Lotov, N. G. Orlova

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
English version PDF (170 kB) Citations (7)
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DOI: https://doi.org/10.1070/SM2003v194n06ABEH000746
Abstract: Exact expressions are obtained for the distribution of the total number of crossings of a strip by sample paths of a random walk whose jumps have a two-sided geometric distribution. The distribution of the number of crossings during a finite time interval is found in explicit form for walks with jumps taking the values $\pm1$. A limit theorem is proved for the joint distribution of the number of crossings of an expanding strip on a finite (increasing) time interval and the position of the walk at the end of this interval, and the corresponding limit distribution is found.
Received: 19.03.2002 and 21.03.2003
Russian version:
Matematicheskii Sbornik, 2003, Volume 194, Number 6, Pages 135–146
DOI: https://doi.org/10.4213/sm746
Bibliographic databases:
UDC: 519.21
MSC: Primary 60G50; Secondary 60G40, 60F05
Language: English
Original paper language: Russian
Citation: V. I. Lotov, N. G. Orlova, “On the number of crossings of a strip by sample paths of a random walk”, Mat. Sb., 194:6 (2003), 135–146; Sb. Math., 194:6 (2003), 927–939
Citation in format AMSBIB
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    • This publication is cited in the following 7 articles:
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