This article is cited 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

DOI: 10.4213/tvp3676

 English version: Theory of Probability and its Applications, 2003, 47:3, 469–487

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