Weak Existence for Degenerate Distribution Dependent SDEs with multiplicative Noise -- a pathwise regularization approach
Probability
2025-09-05 v1 Classical Analysis and ODEs
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.
Cite
@article{arxiv.2509.03665,
title = {Weak Existence for Degenerate Distribution Dependent SDEs with multiplicative Noise -- a pathwise regularization approach},
author = {Fabian Harang and Chengcheng Ling and Peter H. C. Pang},
journal= {arXiv preprint arXiv:2509.03665},
year = {2025}
}
Comments
18 pages