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.
Citation
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
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