Isotropic stochastic flow of homeomorphisms on associated with the critical Sobolev exponent

Dejun Luo

Stochastic Processes and their Applications, 2008, vol. 118, issue 8, 1463-1488

Abstract: We consider the critical Sobolev isotropic Brownian flow in . On the basis of the work of LeJan and Raimond [Y. LeJan, O. Raimond, Integration of Brownian vector fields, Ann. Probab. 30 (2002) 826-873], we prove that the corresponding flow is a flow of homeomorphisms. As an application, we construct an explicit solution, which is also unique in a certain space, to the stochastic transport equation when the associated Gaussian vector fields are divergence free.

Keywords: Isotropic; flow; Stochastic; differential; equation; Non-Lipschitz; condition; Limit; theorem; Stochastic; transport; equation (search for similar items in EconPapers)
Date: 2008
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