English

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.

Keywords

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

R2 v1 2026-07-01T05:19:55.965Z