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arXiv · 2507.21592

Strong solutions of SDE's with rough coefficients

Ali Suleyman Ustunel
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Abstract

We give a proof of the strong existence and the regularity of stochastic differential equations driven by a Brownian motion and a measurable, Markovian drift without no regularity hypothesis except that the Girsanov exponential associated is in some L^{1+{\epsilon}}(\mu) for some fixed {\epsilon}>0 by using the techniques which are totally novel originating from the abstract Wiener space, in particular the solution is an H-C-regular map in the sense of the theory of Leonard Gross.

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Ali Suleyman Ustunel. 2025-07-29. Strong solutions of SDE's with rough coefficients. https://arxiv.org/abs/2507.21592

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