Pathwise uniqueness and continuous dependence for SDEs with nonregular drift

Details Pathwise uniqueness and continuous dependence for SDEs with nonregular drift Pathwise uniqueness and continuous dependence for SDEs with nonregular drift

2010-04-20

arxiv.org/abs/1004.3485v1

Stochastics 83 (2011), no. 3, 241-257

Mathematics

Probability

Scientific paper

10.1080/17442508.2011.553681

A new proof of a pathwise uniqueness result of Krylov and R\"{o}ckner 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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