Abstract
We consider the discrete Wiener-Hopf equation with inhomogeneous term \(g = \{ {g_j}\} _{j = 0}^\infty \in {l_\infty }\); the kernel of the equation is an arithmetic probability distribution generating a random walk drifting to +∞. We prove that the previously obtained formula for the Wiener-Hopf equation with general arithmetic kernel for g ∈ l1 is a solution to the equation for g ∈ l∞ and that successive approximations converge to the solution. The asymptotics of the solution is established in the following cases with account taken of their peculiarities: (1) g ∈ l1; (2) g ∈ l∞; (3) gj → const as j → ∞; (4) g ∉ l1 and gj ↓ 0 as j → ∞.
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Russian Text © The Author(s), 2020, published in Sibirskii Matematicheskii Zhurnal, 2020, Vol. 61, No. 2, pp. 408–417.
The author was supported by the Program of Basic Scientific Research of the Siberian Branch of the Russian Academy of Sciences (Grant No. I.1.2, Project 0314-2019-0005).
The author is grateful to the referee for a careful reading of the manuscript and making very valuable remarks.
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Sgibnev, M.S. The Discrete Wiener-Hopf Equation Whose Kernel is a Probability Distribution with Positive Drift. Sib Math J 61, 322–329 (2020). https://doi.org/10.1134/S0037446620020147
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DOI: https://doi.org/10.1134/S0037446620020147