Strong solutions of SDE's with rough coefficients

2025/07/29 by Ustunel, Ali Suleyman
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2507.21592

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+ε(μ) for some fixed ε>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.

Citations

• SDEs with critical time dependent drifts: strong solutions
• Variational calculus for diffusions
• Variational Calculation of Laplace transforms via Entropy on Wiener Space and some Applications
• Analysis on Wiener Space and Applications
• Entropy, Invertibility and Variational Calculus of the Adapted Shifts on Wiener space
• Uniqueness of solutions of stochastic differential equations

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