An asymptotic property of the solution to the homogeneous generalized Wiener-Hopf equation
type: Item
instance of: scholarly article
title: An asymptotic property of the solution to the homogeneous generalized Wiener-Hopf equation
zbMATH Open document ID: 1221.45011
published in: Siberian Mathematical Journal
publication date: 2011-06-08T00:00:00Z
review text: The following homogeneous generalized Wiener-Hopf equation is considered \[ S(x) = \int_{-\infty}^x {S(x - y)F(dy)},\quad x \geq 0. \tag{1} \] Here \(F\) is a probability distribution on \(\mathbb R\) with zero mean, finite variance, and infinite moment \(\int_{0}^{\infty } x^{3} F(dy)\). The author establishes that the \(P^*\)-solution \(S(x)\) of (1) enjoys the property \[ S(x) - ax \sim b\int_0^x \int_y^\infty \int_v^\infty F((u,\infty ))dudvdy \quad \text{as }x \to \infty, \] where \(a\) and \(b\) are explicit positive constants.
reviewed by: Alexander N. Tynda
Mathematics Subject Classification ID: 45M05
Mathematics Subject Classification ID: 45E10
zbMATH DE Number: 5905398
zbMATH Keywords: Wiener-Hopf integral equation
zbMATH Keywords: asymptotics
author: M. S. Sgibnev
MaRDI profile type: Publication
full work available at URL: s11202-010-0110-8
OpenAlex ID: W2013085391
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DOI: 10.1007/S11202-010-0110-8
description: scientific article; zbMATH DE number 5905398