Journal
ELECTRONIC JOURNAL OF PROBABILITY
Volume 28, Issue -, Pages -Publisher
INST MATHEMATICAL STATISTICS-IMS
DOI: 10.1214/23-EJP913
Keywords
SDEs with singular coefficients; stability; Krylov-Rockner condition; distributional drifts; McKean-Vlasov equations; strong compactness of solutions; Wong-Zakai theorem
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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.
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.
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