Proceedings of the Japan Academy, Series A, Mathematical Sciences

Asymptotic behavior of Lévy measure density corresponding to inverse local time

Tomoko Takemura and Matsuyo Tomisaki

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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.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 91, Number 1 (2015), 9-13.

Dates
First available in Project Euclid: 5 January 2015

Permanent link to this document
https://projecteuclid.org/euclid.pja/1420466272

Digital Object Identifier
doi:10.3792/pjaa.91.9

Mathematical Reviews number (MathSciNet)
MR3296593

Zentralblatt MATH identifier
1325.60130

Subjects
Primary: 60J75: Jump processes
Secondary: 60J55: Local time and additive functionals 60J60: Diffusion processes [See also 58J65]

Keywords
Lévy measure density asymptotic behavior inverse local time

Citation

Takemura, Tomoko; Tomisaki, Matsuyo. Asymptotic behavior of Lévy measure density corresponding to inverse local time. Proc. Japan Acad. Ser. A Math. Sci. 91 (2015), no. 1, 9--13. doi:10.3792/pjaa.91.9. https://projecteuclid.org/euclid.pja/1420466272


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