Integration of Brownian vector fields

Yves Le Jan; Olivier Raimond

doi:10.1214/aop/1023481009

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Home > Journals > Ann. Probab. > Volume 30 > Issue 2 > Article

April 2002 Integration of Brownian vector fields

Yves Le Jan, Olivier Raimond

Ann. Probab. 30(2): 826-873 (April 2002). DOI: 10.1214/aop/1023481009

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Abstract

Using the Wiener chaos decomposition, we show that strong solutions of non-Lipschitzian stochastic differential equations are given by random Markovian kernels. The example of Sobolev flows is studied in some detail, exhibiting interesting phase transitions.

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Yves Le Jan. Olivier Raimond. "Integration of Brownian vector fields." Ann. Probab. 30 (2) 826 - 873, April 2002. https://doi.org/10.1214/aop/1023481009

Information

Published: April 2002

First available in Project Euclid: 7 June 2002

zbMATH: 1037.60061

MathSciNet: MR1905858

Digital Object Identifier: 10.1214/aop/1023481009

Subjects:

Primary: 31C25 , 60H10 , 76F05

Keywords: Coalescence , Dirichlet form , isotropic Brownian flow , Stochastic differential equations , stochastic flow , Strong solution , Wiener chaos decomposition