Pathwise uniqueness and continuous dependence for SDEs with nonregular drift

2010/04/20 by E. Fedrizzi, F. Flandoli · 1 citation
Mathematics · #math.PR #msc:60H10 #msc:60J60

paper · pdf · doi:10.1080/17442508.2011.553681

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

arxiv created 2010/04/20 · arxiv updated 2012/01/20

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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