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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
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
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
Linking options:
https://www.mathnet.ru/eng/tvp3676https://doi.org/10.4213/tvp3676 https://www.mathnet.ru/eng/tvp/v47/i3/p452
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