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Sibirskii Matematicheskii Zhurnal, 2010, Volume 51, Number 6, Pages 1430–1434
(Mi smj2171)
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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
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
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
Linking options:
https://www.mathnet.ru/eng/smj2171 https://www.mathnet.ru/eng/smj/v51/i6/p1430
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