Exit times densities of the Bessel process
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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.References
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Additional Information
- Grzegorz Serafin
- Affiliation: Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, ul. Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
- MR Author ID: 986975
- Email: grzegorz.serafin@pwr.edu.pl
- 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
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 3165-3178
- MSC (2010): Primary 60J60, 60J65
- DOI: https://doi.org/10.1090/proc/13419
- MathSciNet review: 3637962