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Exit probability levels of diffusion processes


Author: Doncho S. Donchev
Journal: Proc. Amer. Math. Soc. 145 (2017), 2241-2253
MSC (2010): Primary 60J60
DOI: https://doi.org/10.1090/proc/13392
Published electronically: January 27, 2017
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Abstract: We are interested in the probability that a diffusion process exits a domain between two curved boundaries through the upper one. In case of given boundaries that problem has closed solutions only in some special cases. We study a modification of the problem in which not only the exit probabilities but also the boundaries are unknown. Introducing the notion of exit probability levels, we show that this new problem can be reduced to a single non-linear second order PDE. In case of some important diffusion processes we find large families of solutions to this equation.


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Additional Information

Doncho S. Donchev
Affiliation: Faculty of Mathematics and Informatics, St. Kliment Ohridski University of Sofia, 5, James Bourchier Str., 1164 Sofia, Bulgaria
Email: doncho@fmi.uni-sofia.bg

DOI: https://doi.org/10.1090/proc/13392
Received by editor(s): July 10, 2014
Received by editor(s) in revised form: July 6, 2016, and July 15, 2016
Published electronically: January 27, 2017
Communicated by: Mourad Ismail
Article copyright: © Copyright 2017 American Mathematical Society