Stability estimates for singular SDEs and applications

We prove several stability estimates, comparing solutions driven by different (b(i), sigma(i)), both for Ito and Stratonovich SDEs, possibly depending on negative Sobolev norms of the difference b(1) - b(2). We then discuss several applications of these results to McKean-Vlasov SDEs, criteria for strong compactness of solutions and Wong-Zakai type theorems.

Automated summary

In this paper, we prove several stability estimates for comparing solutions driven by different (b(i), sigma(i)) in both Ito and Stratonovich SDEs. These estimates may depend on negative Sobolev norms of the difference b(1) - b(2). We also discuss several applications of these results to McKean-Vlasov SDEs, criteria for strong compactness of solutions, and Wong-Zakai type theorems.