带有分数拉普拉卡的非线性福克-普朗克方程和带有莱维噪声的麦肯-弗拉索夫 SDEs

IF 1.5 1区数学 Q2 STATISTICS & PROBABILITY

Probability Theory and Related Fields Pub Date : 2024-04-12 DOI:10.1007/s00440-024-01277-1

Viorel Barbu, Michael Röckner

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引用次数: 0

摘要

这项工作关注的是：在 \(s\in \left( \frac{1}{2},1\right) \) 条件下，分数拉普拉斯算子 \((- \Delta )^s\) 非线性福克-普朗克方程温和解的存在性。在适当的扩散和漂移项假设下，施瓦茨分布解的唯一性也得到了证明。作为应用，证明了具有莱维噪声的麦金-弗拉索夫方程的弱存在性和唯一性解，以及它们的马尔可夫性质。

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Nonlinear Fokker–Planck equations with fractional Laplacian and McKean–Vlasov SDEs with Lévy noise

This work is concerned with the existence of mild solutions to nonlinear Fokker–Planck equations with fractional Laplace operator \((- \Delta )^s\) for \(s\in \left( \frac{1}{2},1\right) \). The uniqueness of Schwartz distributional solutions is also proved under suitable assumptions on diffusion and drift terms. As applications, weak existence and uniqueness of solutions to McKean–Vlasov equations with Lévy noise, as well as the Markov property for their laws are proved.

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来源期刊

Probability Theory and Related Fields 数学-统计学与概率论

CiteScore

3.70

自引率

5.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Probability Theory and Related Fields publishes research papers in modern probability theory and its various fields of application. Thus, subjects of interest include: mathematical statistical physics, mathematical statistics, mathematical biology, theoretical computer science, and applications of probability theory to other areas of mathematics such as combinatorics, analysis, ergodic theory and geometry. Survey papers on emerging areas of importance may be considered for publication. The main languages of publication are English, French and German.