Article2013

Hölder Flow and Differentiability for SDEs with Nonregular Drift

72 citations0/0 files storedStochastic Analysis and Applications

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Stochastic processes and financial applications Mathematical Dynamics and Fractals Geometric Analysis and Curvature Flows

Abstract

We prove the existence of a stochastic flow of Hölder homeomorphisms for solutions of SDEs with singular time dependent drift having only certain integrability properties. We also show that the solution map x → X x is differentiable in a weak sense.

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References

2005Stochastic Integration and Differential Equations 1971On the uniqueness of solutions of stochastic differential equations 1974A TRANSFORMATION OF THE PHASE SPACE OF A DIFFUSION PROCESS THAT REMOVES THE DRIFT 2004Strong solutions of stochastic equations with singular time dependent drift 1996Existence of strong solutions for Itô's stochastic equations via approximations 1981ON STRONG SOLUTIONS AND EXPLICIT FORMULAS FOR SOLUTIONS OF STOCHASTIC INTEGRAL EQUATIONS 2005Strong solutions of SDES with singular drift and Sobolev diffusion coefficients 2011Pathwise uniqueness and continuous dependence for SDEs with non-regular drift

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