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

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  • Luo, Dejun

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.

Suggested Citation

  • Luo, Dejun, 2008. "Isotropic stochastic flow of homeomorphisms on associated with the critical Sobolev exponent," Stochastic Processes and their Applications, Elsevier, vol. 118(8), pages 1463-1488, August.
    • Handle: RePEc:eee:spapps:v:118:y:2008:i:8:p:1463-1488
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    References listed on IDEAS

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    1. Zhang, Xicheng, 2005. "Homeomorphic flows for multi-dimensional SDEs with non-Lipschitz coefficients," Stochastic Processes and their Applications, Elsevier, vol. 115(3), pages 435-448, March.
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