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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Exit probability levels of diffusion processes
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by Doncho S. Donchev PDF
Proc. Amer. Math. Soc. 145 (2017), 2241-2253 Request permission

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
  • MR Author ID: 360190
  • Email: doncho@fmi.uni-sofia.bg
  • 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
  • © Copyright 2017 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 145 (2017), 2241-2253
  • MSC (2010): Primary 60J60
  • DOI: https://doi.org/10.1090/proc/13392
  • MathSciNet review: 3611334