The Annals of Probability

Local time flow related to skew brownian motion

Krzysztof Burdzy and Zhen-Qing Chen

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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.

Article information

Source
Ann. Probab., Volume 29, Number 4 (2001), 1693-1715.

Dates
First available in Project Euclid: 5 March 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1015345768

Digital Object Identifier
doi:10.1214/aop/1015345768

Mathematical Reviews number (MathSciNet)
MR1880238

Zentralblatt MATH identifier
1037.60057

Subjects
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05] 60J65: Brownian motion [See also 58J65]

Keywords
Local time stochastic flow skew Brownian motion

Citation

Burdzy, Krzysztof; Chen, Zhen-Qing. Local time flow related to skew brownian motion. Ann. Probab. 29 (2001), no. 4, 1693--1715. doi:10.1214/aop/1015345768. https://projecteuclid.org/euclid.aop/1015345768


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