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

Fabian Harang; Chengcheng Ling; Peter H. C. Pang

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arXiv · 2509.03665

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

Fabian Harang·Chengcheng Ling·Peter H. C. Pang

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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.

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Fabian Harang, Chengcheng Ling, Peter H. C. Pang. 2025-09-03. Weak Existence for Degenerate Distribution Dependent SDEs with multiplicative Noise -- a pathwise regularization approach. https://arxiv.org/abs/2509.03665

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