Articlegreen2011

Pathwise uniqueness and continuous dependence for SDEs with non-regular drift

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Stochastic processes and financial applications Nonlinear Partial Differential Equations Stochastic processes and statistical mechanics

Abstract

A new proof of a pathwise uniqueness result of Krylov and Röckner is given. It concerns SDEs with drift having only certain integrability properties. In spite of the poor regularity of the drift, pathwise continuous dependence on initial conditions may be obtained, by means of this new proof. The proof is formulated in such a way to show that the only major tool is a good regularity theory for the heat equation forced by a function with the same regularity of the drift.

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References

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

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