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Theory of Probability and Mathematical Statistics

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Convergence of exit times for diffusion processes


Authors: Yu. S. Mishura and V. V. Tomashyk
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 88 (2013).
Journal: Theor. Probability and Math. Statist. 88 (2014), 139-149
MSC (2010): Primary 60G40, 60H15, 60J60
DOI: https://doi.org/10.1090/S0094-9000-2014-00924-2
Published electronically: July 24, 2014
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Abstract: We establish the convergence in probability of exit times from a strip for stochastic processes that are solutions of stochastic differential equations with diffusion coefficients satisfying the Yamada condition under the assumption that the coefficients converge. As an auxiliary result, the uniform convergence in probability of pre-limit processes to the limit process is proved.


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Additional Information

Yu. S. Mishura
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Volodymyrs’ka Street, 64, Kyiv 01601, Ukraine
Email: myus{@}univ.kiev.ua

V. V. Tomashyk
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Volodymyrs’ka Street, 64, Kyiv 01601, Ukraine
Email: vladdislav@gmail.com

DOI: https://doi.org/10.1090/S0094-9000-2014-00924-2
Keywords: Stopping times, stochastic differential equations, Yamada condition
Received by editor(s): November 1, 2012
Published electronically: July 24, 2014
Article copyright: © Copyright 2014 American Mathematical Society