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October 2004 Lenses in skew Brownian flow
Krzysztof Burdzy, Haya Kaspi
Ann. Probab. 32(4): 3085-3115 (October 2004). DOI: 10.1214/009117904000000711


We consider a stochastic flow in which individual particles follow skew Brownian motions, with each one of these processes driven by the same Brownian motion. One does not have uniqueness for the solutions of the corresponding stochastic differential equation simultaneously for all real initial conditions. Due to this lack of the simultaneous strong uniqueness for the whole system of stochastic differential equations, the flow contains lenses, that is, pairs of skew Brownian motions which start at the same point, bifurcate, and then coalesce in a finite time. The paper contains qualitative and quantitative (distributional) results on the geometry of the flow and lenses.


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Krzysztof Burdzy. Haya Kaspi. "Lenses in skew Brownian flow." Ann. Probab. 32 (4) 3085 - 3115, October 2004.


Published: October 2004
First available in Project Euclid: 8 February 2005

zbMATH: 1071.60073
MathSciNet: MR2094439
Digital Object Identifier: 10.1214/009117904000000711

Primary: 60J65
Secondary: 60G17 , 60H10 , 60J55

Keywords: skew Brownian motion , stochastic flow

Rights: Copyright © 2004 Institute of Mathematical Statistics


Vol.32 • No. 4 • October 2004
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