English

Distribution dependent SDEs driven by additive continuous noise

Probability 2022-03-07 v1 Analysis of PDEs

Abstract

We study distribution dependent stochastic differential equation driven by a continuous process, without any specification on its law, following the approach initiated in [16]. We provide several criteria for existence and uniqueness of solutions which go beyond the classical globally Lipschitz setting. In particular we show well-posedness of the equation, as well as almost sure convergence of the associated particle system, for drifts satisfying either Osgood-continuity, monotonicity, local Lipschitz or Sobolev differentiability type assumptions.

Keywords

Cite

@article{arxiv.2105.14056,
  title  = {Distribution dependent SDEs driven by additive continuous noise},
  author = {Lucio Galeati and Fabian A. Harang and Avi Mayorcas},
  journal= {arXiv preprint arXiv:2105.14056},
  year   = {2022}
}

Comments

39 pages

R2 v1 2026-06-24T02:35:11.176Z