具有nemytskii型系数的McKean-Vlasov SDEs的强解

IF 0.5 4区数学 Q4 STATISTICS & PROBABILITY

Electronic Communications in Probability Pub Date : 2021-07-15 DOI:10.1214/23-ECP519

Sebastian Grube

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引用次数: 3

摘要

我们用nemytskii型的方法研究了一类漂移系数和扩散系数依赖于解的时间边际律密度的McKean-Vlasov SDEs。这类McKean-Vlasov SDE来源于相关非线性FPKE的研究，已知存在有界sobolev -正则schwarz -分布解u。通过叠加原理，已知存在具有时间边际密度u的McKean-Vlasov SDE的弱解。我们证明存在McKean-Vlasov SDE的强解。主要工具是SDEs的受限Yamada-Watanabe定理，该定理是在经典Yamada-Watanabe定理的证明中通过观察得到的。

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Strong solutions to McKean–Vlasov SDEs with coefficients of Nemytskii-type

We study a large class of McKean-Vlasov SDEs with drift and diffusion coefficient depending on the density of the solution's time marginal laws in a Nemytskii-type of way. A McKean-Vlasov SDE of this kind arises from the study of the associated nonlinear FPKE, for which is known that there exists a bounded Sobolev-regular Schwartz-distributional solution u. Via the superposition principle, it is already known that there exists a weak solution to the McKean-Vlasov SDE with time marginal densities u. We show that there exists a strong solution the McKean-Vlasov SDE, which is unique among weak solutions with time marginal densities u. The main tool is a restricted Yamada-Watanabe theorem for SDEs, which is obtained by an observation in the proof of the classic Yamada-Watanabe theorem.

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来源期刊

Electronic Communications in Probability 工程技术-统计学与概率论

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Electronic Communications in Probability (ECP) publishes short research articles in probability theory. Its sister journal, the Electronic Journal of Probability (EJP), publishes full-length articles in probability theory. Short papers, those less than 12 pages, should be submitted to ECP first. EJP and ECP share the same editorial board, but with different Editors in Chief.