Geodesic
Absorption probability at the border of a random walk in a quadrant and a branching process with interaction of particles
Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 3, pp. 452-474

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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, Chebyshev polynomials.
Mots-clés : exact solutions 
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     author = {A. V. Kalinkin},
     title = {Absorption probability at the border of a random walk in a quadrant and a branching process with interaction of particles},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {452--474},
     publisher = {mathdoc},
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     number = {3},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2002_47_3_a1/}
}
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A. V. Kalinkin. Absorption probability at the border of a random walk in a quadrant and a branching process with interaction of particles. Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 3, pp. 452-474. http://geodesic.mathdoc.fr/item/TVP_2002_47_3_a1/