On subexponentiality of the Lévy measure of the diffusion inverse local time; with applications to penalizations

Paavo Salminen; Pierre Vallois

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arXiv · 0805.4353

On subexponentiality of the Lévy measure of the diffusion inverse local time; with applications to penalizations

Paavo Salminen·Pierre Vallois

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Abstract

For a recurrent linear diffusion on $\R_+$ we study the asymptotics of the distribution of its local time at 0 as the time parameter tends to infinity. Under the assumption that the Lévy measure of the inverse local time is subexponential this distribution behaves asymtotically as a multiple of the Lévy measure. Using spectral representations we find the exact value of the multiple. For this we also need a result on the asymptotic behavior of the convolution of a subexponential distribution and an arbitrary distribution on $\R_+.$ The exact knowledge of the asymptotic behavior of the distribution of the local time allows us to analyze the process derived via a penalization procedure with the local time. This result generalizes the penalizations obtained in Roynette, Vallois and Yor \cite{rvyV} for Bessel processes.

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BibTeX RIS

Paavo Salminen, Pierre Vallois. 2008-05-28. On subexponentiality of the Lévy measure of the diffusion inverse local time; with applications to penalizations. https://arxiv.org/abs/0805.4353

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