This article is cited in 4 papers

The discrete Wiener–Hopf equation with probability kernel of oscillating type

M. S. Sgibnev

Sobolev Institute of Mathematics, Novosibirsk, Russia

Abstract: We prove the existence of a solution to the discrete inhomogeneous Wiener–Hopf equation whose kernel is an arithmetic probability distribution generating an oscillating random walk. Asymptotic properties of the solution are established depending on the properties of the inhomogeneous term of the equation and its kernel.

Keywords: discrete Wiener-Hopf equation, inhomogeneous equation, asymptotic behavior, arithmetic distribution, oscillating type.

UDC: 517.968.2

Received: 23.08.2018
Revised: 04.12.2018
Accepted: 19.12.2018

DOI: 10.33048/smzh.2019.60.314

 English version: Siberian Mathematical Journal, 2019, 60:3, 516–525

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