论文标题
单数SDE和应用的稳定性估计
Stability estimates for singular SDEs and applications
论文作者
论文摘要
我们考虑具有单数漂移$ b $的多维SDE和Sobolev扩散系数$σ$，可以满足Krylov-Röckner型假设。我们证明了几项稳定性估计值，比较了由ITô和Stratonovich SDE的不同$（B^i，σ^i）$驱动的解决方案，这可能取决于差异的负sobolev规范$ b^1-b^2 $。然后，我们将这些结果的几种应用与McKean-Vlasov Sdes，解决方案紧凑性和Wong-Zakai型定理的标准。
We consider multidimensional SDEs with singular drift $b$ and Sobolev diffusion coefficients $σ$, satisfying Krylov--Röckner type assumptions. We prove several stability estimates, comparing solutions driven by different $(b^i,σ^i)$, 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.
