Stability estimates for singular SDEs and applications

Abstract

We prove several stability estimates, comparing solutions driven by different $(b^i,{\mathit{\sigma }}^i)$, both for Itô 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.