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May 2013 Distance between two skew Brownian motions as a S.D.E. with jumps and law of the hitting time
Arnaud Gloter, Miguel Martinez
Ann. Probab. 41(3A): 1628-1655 (May 2013). DOI: 10.1214/12-AOP776

Abstract

In this paper, we consider two skew Brownian motions, driven by the same Brownian motion, with different starting points and different skewness coefficients. We show that we can describe the evolution of the distance between the two processes with a stochastic differential equation. This S.D.E. possesses a jump component driven by the excursion process of one of the two skew Brownian motions. Using this representation, we show that the local time of two skew Brownian motions at their first hitting time is distributed as a simple function of a Beta random variable. This extends a result by Burdzy and Chen [Ann. Probab. 29 (2001) 1693–1715], where the law of coalescence of two skew Brownian motions with the same skewness coefficient is computed.

Citation

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Arnaud Gloter. Miguel Martinez. "Distance between two skew Brownian motions as a S.D.E. with jumps and law of the hitting time." Ann. Probab. 41 (3A) 1628 - 1655, May 2013. https://doi.org/10.1214/12-AOP776

Information

Published: May 2013
First available in Project Euclid: 29 April 2013

zbMATH: 1296.60149
MathSciNet: MR3098686
Digital Object Identifier: 10.1214/12-AOP776

Subjects:
Primary: 60H10
Secondary: 60J55, 60J65

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.41 • No. 3A • May 2013
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