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Sibirskii Matematicheskii Zhurnal, 2010, Volume 51, Number 6, Pages 1430–1434 (Mi smj2171)  

This article is cited in 1 scientific paper (total in 1 paper)

An asymptotic property of the solution to the homogeneous generalized Wiener–Hopf equation

M. S. Sgibnev

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
Full-text PDF (281 kB) Citations (1)
References:
Abstract: We consider the homogeneous generalized Wiener–Hopf equation
$$ S(x)=\int^x_{-\infty}S(x-y)F(dy),\qquad x\ge0, $$
wehere $F$ is a probability distribution on $\mathbb R$ with zero mean, finite variance, and infinite moment $\int^\infty_0x^3F(dy)$. Its $P^*$-solution $S(x)$ enjoys the property
$$ S(x)-ax\sim b\int^x_0\int^\infty_y\int^\infty_vF((u,\infty))\,dudvdy\qquad\text{as}\quad x\to\infty, $$
where $a$ and $b$ are explicit positive constants.
Keywords: integral equation, homogeneous equation, Wiener–Hopf equation, solution, asymptotics.
Received: 01.12.2009
English version:
Siberian Mathematical Journal, 2010, Volume 51, Issue 6, Pages 1131–1134
DOI: https://doi.org/10.1007/s11202-010-0110-8
Bibliographic databases:
Document Type: Article
UDC: 517.968
Language: Russian
Citation: M. S. Sgibnev, “An asymptotic property of the solution to the homogeneous generalized Wiener–Hopf equation”, Sibirsk. Mat. Zh., 51:6 (2010), 1430–1434; Siberian Math. J., 51:6 (2010), 1131–1134
Citation in format AMSBIB
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\paper An asymptotic property of the solution to the homogeneous generalized Wiener--Hopf equation
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\vol 51
\issue 6
\pages 1430--1434
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\jour Siberian Math. J.
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\vol 51
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\pages 1131--1134
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  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Сибирский математический журнал Siberian Mathematical Journal
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