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Exit times densities of the Bessel process


Author: Grzegorz Serafin
Journal: Proc. Amer. Math. Soc. 145 (2017), 3165-3178
MSC (2010): Primary 60J60, 60J65
DOI: https://doi.org/10.1090/proc/13419
Published electronically: January 6, 2017
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Abstract: We examine the density functions of the first exit times of the Bessel process from the intervals $ [0,1)$ and $ (0,1)$. First, we express them by means of the transition density function of the killed process. Using that relationship we provide precise estimates and asymptotics of the exit time densities. In particular, the results hold for the first exit time of the $ n$-dimensional Brownian motion from a ball.


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Grzegorz Serafin
Affiliation: Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, ul. Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
Email: grzegorz.serafin@pwr.edu.pl

DOI: https://doi.org/10.1090/proc/13419
Keywords: Bessel process, exit time density, sharp estimate, asymptotics, Brownian motion, ball
Received by editor(s): May 28, 2015
Received by editor(s) in revised form: June 4, 2016, and August 5, 2016
Published electronically: January 6, 2017
Additional Notes: This project was funded by the MNiSW grant no. IP2012018472.
Communicated by: Mark M. Meerschaert
Article copyright: © Copyright 2017 American Mathematical Society