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

2008/05/28 by Paavo Salminen, Salminen, Paavo, Pierre Vallois +1 · 1 citation
Economics, Econometrics and Finance · Mathematics · #60J30 #60J60 #60J65 #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #msc:60J30 #msc:60J60 #msc:60J65

paper · pdf · doi:10.48550/arxiv.0805.4353

arxiv created 2008/05/28 · openalex publication_date 2008/05/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \citervyV for Bessel processes.

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