奇异SDE的稳定性估计及其应用

IF 1.3 3区数学 Q2 STATISTICS & PROBABILITY

Electronic Journal of Probability Pub Date : 2022-08-07 DOI:10.1214/23-ejp913

L. Galeati, Chengcheng Ling

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引用次数: 4

摘要

我们考虑具有奇异漂移$b$和Sobolev扩散系数$\sigma$的多维SDE，满足Krylov-R\“ockner型假设。我们证明了几个稳定性估计，比较了不同$（b^i，\ sigma^i）驱动的解$，对于It\^o和Stratonovich SDE，可能取决于差值$b^1-b^2$的负Sobolev范数。然后我们讨论了这些结果在McKean—Vlasov SDE、解的强紧性准则和Wong—Zakai型定理中的几个应用。

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Stability estimates for singular SDEs and applications

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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来源期刊

Electronic Journal of Probability 数学-统计学与概率论

CiteScore

1.80

自引率

7.10%

发文量

119

审稿时长

4-8 weeks

期刊介绍： The Electronic Journal of Probability publishes full-size research articles in probability theory. The Electronic Communications in Probability (ECP), a sister journal of EJP, publishes short notes and research announcements in probability theory. Both ECP and EJP are official journals of the Institute of Mathematical Statistics and the Bernoulli society.