Flow of Homeomorphisms and Stochastic Transport Equations

DOI10.1080/07362990701540568zbMath1125.60083OpenAlexW2001921690MaRDI QIDQ5421609

Shizan Fang, De Jun Luo

Publication date: 24 October 2007

Published in: Stochastic Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/07362990701540568

zbMATH Keywords

stochastic differential equationWong-Zakai approximationnon-Lipschitz conditionstochastic transport equationflow of homeomorphisms

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Diffusion processes (60J60)

Related Items (14)

Stochastic transport equation with bounded and Dini continuous drift ⋮ Stochastic flows and Bismut formulas for stochastic Hamiltonian systems ⋮ Transport equation driven by a stochastic measure ⋮ Quasi-invariance of the stochastic flow associated to Itô's SDE with singular time-dependent drift ⋮ Pathwise uniqueness of multi-dimensional stochastic differential equations with Hölder diffusion coefficients ⋮ Stochastic flows of SDEs with non-Lipschitz coefficients and singular time ⋮ Quasi-Invariant Flow Generated by Stratonovich SDE with BV Drift Coefficient ⋮ Isotropic stochastic flow of homeomorphisms on \(\mathbb R^d\) associated with the critical Sobolev exponent ⋮ Stochastic flows of SDEs with irregular coefficients and stochastic transport equations ⋮ Flow of diffeomorphisms for SDEs with unbounded Hölder continuous drift ⋮ Stochastic Lagrangian flows on the group of volume-preserving homeomorphisms of the spheres ⋮ Stochastic regularization for transport equations ⋮ The second-order parabolic PDEs with singular coefficients and applications ⋮ Quasi-invariance of Lebesgue measure under the homeomorphic flow generated by SDE with non-Lipschitz coefficient

Cites Work

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• Global flows for stochastic differential equations without global Lipschitz conditions
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• Strong solutions of stochastic equations with singular time dependent drift
• Integration of Brownian vector fields.
• Homeomorphic flows for multi-dimensional SDEs with non-Lipschitz coefficients
• Isotropic stochastic flow of homeomorphisms on \(S^{d}\) for the critical Sobolev exponent
• Strong solutions of SDEs with singular drift and Sobolev diffusion coefficients
• A study of a class of stochastic differential equations with non-Lipschitzian coefficients
• Flows of stochastic dynamical systems: The functional analytic approach
• On the strong comparison theorems for solutions of stochastic differential equations
• Passive scalar equation in a turbulent incompressible Gaussian velocity field

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