Weak Existence for Degenerate Distribution Dependent SDEs with multiplicative Noise -- a pathwise regularization approach

2025/09/03 by Harang, Fabian, Ling, Chengcheng, Pang, Peter H. C.
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2509.03665

Abstract

We establish the existence of weak solutions to a class of distribution-dependent stochastic differential equations (DDSDEs) with possibly degenerate multiplicative noise and singular coefficients. Extending the weak existence techniques introduced by Bechtold & Hofmanova 2023 to a distribution-dependent framework, we utilize pathwise averaging and local-time decomposition methods to show how irregular noise effectively regularizes analytical challenges associated with degeneracies in stochastic systems.

Citations

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Related

• Weak solutions for singular multiplicative SDEs via regularization by noise
• Distribution-Path Dependent Nonlinear SPDEs with Application to Stochastic Transport Type Equations
• Well-posedness for SDEs driven by different type of noises
• Weak well-posedness for degenerate SDEs driven by Lévy processes
• Distribution Dependent SDEs with Singular Coefficients