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January 2015 Asymptotic behavior of Lévy measure density corresponding to inverse local time
Tomoko Takemura, Matsuyo Tomisaki
Proc. Japan Acad. Ser. A Math. Sci. 91(1): 9-13 (January 2015). DOI: 10.3792/pjaa.91.9

Abstract

For a one dimensional diffusion process $\mathbf{D}^{*}_{s,m}$ and the harmonic transformed process $\mathbf{D}^{*}_{s_{h},m_{h}}$, the asymptotic behavior of the Lévy measure density corresponding to the inverse local time at the regular end point is investigated. The asymptotic behavior of $n^{*}$, the Lévy measure density corresponding to $\mathbf{D}^{*}_{s,m}$, follows from asymptotic behavior of the speed measure $m$. However, that of $n^{h*}$, the Lévy measure density corresponding to $\mathbf{D}^{*}_{s_{h},m_{h}}$, is given by a simple form, $n^{*}$ multiplied by an exponential decay function, for any harmonic function $h$ based on the original diffusion operator.

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Tomoko Takemura. Matsuyo Tomisaki. "Asymptotic behavior of Lévy measure density corresponding to inverse local time." Proc. Japan Acad. Ser. A Math. Sci. 91 (1) 9 - 13, January 2015. https://doi.org/10.3792/pjaa.91.9

Information

Published: January 2015
First available in Project Euclid: 5 January 2015

zbMATH: 1325.60130
MathSciNet: MR3296593
Digital Object Identifier: 10.3792/pjaa.91.9

Subjects:
Primary: 60J75
Secondary: 60J55, 60J60

Rights: Copyright © 2015 The Japan Academy

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Vol.91 • No. 1 • January 2015
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