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Teoriya Veroyatnostei i ee Primeneniya, 2002, Volume 47, Issue 3, Pages 452–474
DOI: https://doi.org/10.4213/tvp3676 (Mi tvp3676) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Absorption probability at the border of a random walk in a quadrant and a branching process with interaction of particles

A. V. Kalinkin

N. E. Bauman Moscow State Technical University
Full-text PDF (2091 kB) Citations (1)
DOI: https://doi.org/10.4213/tvp3676
Abstract: Simple integral representations are obtained for the absorption probability at a boundary point of a random walk on the integer-valued lattice of a quadrant under various hypotheses about the distribution of the jumps of the random walk. To get the representations we apply the method of exponential generating function for solving a stationary first (backward) system of Kolmogorov differential equations suggested in [A. V. Kalinkin, Theory Probab. Appl., 27 (1982), pp. 201–205] and [A. V. Kalinkin, Sov. Math. Dokl., 27 (1983), pp. 493–497].
Keywords: absorption probability of a random walk, branching process, exponential generating function, hyperbolic type partial differential equation, Darboux–Picard problem, exact solutions, Chebyshev polynomials.
Received: 08.09.2000
English version:
Theory of Probability and its Applications, 2003, Volume 47, Issue 3, Pages 469–487
DOI: https://doi.org/10.1137/S0040585X97979810
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. V. Kalinkin, “Absorption probability at the border of a random walk in a quadrant and a branching process with interaction of particles”, Teor. Veroyatnost. i Primenen., 47:3 (2002), 452–474; Theory Probab. Appl., 47:3 (2003), 469–487
Citation in format AMSBIB
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\by A.~V.~Kalinkin
\paper Absorption probability at the border of a random walk in a quadrant and a branching process with interaction of particles
\jour Teor. Veroyatnost. i Primenen.
\yr 2002
\vol 47
\issue 3
\pages 452--474
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\zmath{https://zbmath.org/?q=an:1036.60061}
\transl
\jour Theory Probab. Appl.
\yr 2003
\vol 47
\issue 3
\pages 469--487
\crossref{https://doi.org/10.1137/S0040585X97979810}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000185370300006}
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  • https://www.mathnet.ru/eng/tvp3676
  • https://doi.org/10.4213/tvp3676
  • https://www.mathnet.ru/eng/tvp/v47/i3/p452
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
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