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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

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

Rights: Copyright © 2002 Institute of Mathematical Statistics

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Vol.30 • No. 2 • April 2002
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