乘性稳定噪声驱动下McKean-Vlasov SDEs的适定性

IF 0.9 3区数学 Q2 MATHEMATICS

Acta Mathematica Sinica-English Series Pub Date : 2025-05-15 DOI:10.1007/s10114-025-4030-8

Changsong Deng, Xing Huang

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引用次数: 0

摘要

建立了一类由对称α-稳定lsamvy过程（\({1 \over 2} <\alpha \leq 1\)）驱动的McKean-Vlasov SDEs的适定性，其中漂移系数在空间变量上是Hölder连续的，噪声系数在空间变量上是Lipscitz连续的，并且它们在分布变量上都满足关于Wasserstein距离的Lipschitz条件。如果漂移系数不依赖于分布变量，则本文开发的方法适用于α∈(0,1)的情况。主要工具依赖于（分布无关的）稳定SDEs的热核估计和Banach不动点定理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Well-Posedness for McKean–Vlasov SDEs Driven by Multiplicative Stable Noises

We establish the well-posedness for a class of McKean–Vlasov SDEs driven by symmetric α-stable Lévy processes (\({1 \over 2} <\alpha \leq 1\)), where the drift coefficient is Hölder continuous in space variable, while the noise coefficient is Lipscitz continuous in space variable, and both of them satisfy the Lipschitz condition in distribution variable with respect to Wasserstein distance. If the drift coefficient does not depend on distribution variable, our methodology developed in this paper applies to the case α ∈ (0, 1]. The main tool relies on heat kernel estimates for (distribution independent) stable SDEs and Banach’s fixed point theorem.

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来源期刊

Acta Mathematica Sinica-English Series 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

138

审稿时长

14.5 months

期刊介绍： Acta Mathematica Sinica, established by the Chinese Mathematical Society in 1936, is the first and the best mathematical journal in China. In 1985, Acta Mathematica Sinica is divided into English Series and Chinese Series. The English Series is a monthly journal, publishing significant research papers from all branches of pure and applied mathematics. It provides authoritative reviews of current developments in mathematical research. Contributions are invited from researchers from all over the world.