English

Strong solutions of SDE's with rough coefficients

Probability 2025-08-05 v2

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.

Keywords

Cite

@article{arxiv.2507.21592,
  title  = {Strong solutions of SDE's with rough coefficients},
  author = {Ali Suleyman Ustunel},
  journal= {arXiv preprint arXiv:2507.21592},
  year   = {2025}
}

Comments

Some typos corrected and notations better explained