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October 2001 Local time flow related to skew brownian motion
Krzysztof Burdzy, Zhen-Qing Chen
Ann. Probab. 29(4): 1693-1715 (October 2001). DOI: 10.1214/aop/1015345768

Abstract

We define a local time flow of skew Brownian motions ,that is, a family of solutions to the stochastic differential equation defining the skew Brownian motion, starting from different points but driven by the same Brownian motion. We prove several results on distributional and path properties of the flow. Our main result is a version of the Ray–Knight theorem on local times. In our case, however, the local time process viewed as a function of the spatial variable is a pure jump Markov process rather than a diffusion.

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Krzysztof Burdzy. Zhen-Qing Chen. "Local time flow related to skew brownian motion." Ann. Probab. 29 (4) 1693 - 1715, October 2001. https://doi.org/10.1214/aop/1015345768

Information

Published: October 2001
First available in Project Euclid: 5 March 2002

zbMATH: 1037.60057
MathSciNet: MR1880238
Digital Object Identifier: 10.1214/aop/1015345768

Subjects:
Primary: 60H10 , 60J65

Keywords: Local time , skew Brownian motion , stochastic flow

Rights: Copyright © 2001 Institute of Mathematical Statistics

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Vol.29 • No. 4 • October 2001
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