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

Journal Article · Mon Jun 30 00:00:00 EDT 2003 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2003V194N06ABEH000746; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)· OSTI ID:21208317

Lotov, V I; Orlova, N G ^[1]

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1. S.L. Sobolev Institute for Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk (Russian Federation)

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 {+-}1. 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.

• OSTI ID: 21208317
• Journal Information: Sbornik. Mathematics, Vol. 194, Issue 6; Other Information: DOI: 10.1070/SM2003v194n06ABEH000746; Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
EXACT SOLUTIONS
GRAPH THEORY
RANDOMNESS