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


 
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1. Title Title of document On subexponentiality of the Lévy measure of the inverse local time; with applications to penalizations
 
2. Creator Author's name, affiliation, country Paavo H Salminen; AAbo Akademi University, Mathematical Department
 
2. Creator Author's name, affiliation, country Pierre Vallois; Université Henri Poincaré, Département de Mathématique
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Brownian motion, Bessel process, Hitting time, Tauberian theorem, excursions
 
3. Subject Subject classification 60J60, 60J65, 60J30
 
4. Description Abstract Abstract. For a recurrent linear diffusion on the positive real axis 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 asymptotically 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 the positive real axis. 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 by Roynette, Vallois and Yor in Studia Sci. Math. Hungar. 45(1), 2008 for Bessel processes.
 
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7. Date (YYYY-MM-DD) 2009-09-17
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/686
 
10. Identifier Digital Object Identifier 10.1214/EJP.v14-686
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 14
 
12. Language English=en
 
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