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December 2006 Asymptotic conditional distributions related to one-dimensional generalized diffusion processes
Masaru Iizuka, Miyuki Maeno, Matsuyo Tomisaki
Tsukuba J. Math. 30(2): 273-327 (December 2006). DOI: 10.21099/tkbjm/1496165065

Abstract

For a one-dimensional generalized diffusion process $\{X(t) : t \geq O\}$ on an interval $I$, we consider an expectation conditional on no hitting the end points of $I$. If the end points are not accessible, we take two sequences $\{ \xi_{n}\}$ and $\{ \eta_{n} \}$ which converge to the end points as $n \rightarrow \infty$, instead of end points. We obtain the asymptotic behavior of this conditional expectation as $t \rightarrow \infty$ and $n \rightarrow \infty$. As an application of our results, we discuss the asymptotic conditional distribution and related quantities in population genetics.

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Masaru Iizuka. Miyuki Maeno. Matsuyo Tomisaki. "Asymptotic conditional distributions related to one-dimensional generalized diffusion processes." Tsukuba J. Math. 30 (2) 273 - 327, December 2006. https://doi.org/10.21099/tkbjm/1496165065

Information

Published: December 2006
First available in Project Euclid: 30 May 2017

zbMATH: 1122.60068
MathSciNet: MR2271302
Digital Object Identifier: 10.21099/tkbjm/1496165065

Rights: Copyright © 2006 University of Tsukuba, Institute of Mathematics

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Vol.30 • No. 2 • December 2006
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