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arXiv · 2208.03670

Stability estimates for singular SDEs and applications

Lucio Galeati·Chengcheng Ling
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Abstract

We consider multidimensional SDEs with singular drift $b$ and Sobolev diffusion coefficients $\sigma$, satisfying Krylov--R\"ockner type assumptions. We prove several stability estimates, comparing solutions driven by different $(b^i,\sigma^i)$, both for It\^o 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.

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Lucio Galeati, Chengcheng Ling. 2022-08-07. Stability estimates for singular SDEs and applications. https://arxiv.org/abs/2208.03670

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