Open Access
2022 Distribution dependent SDEs driven by additive continuous noise
Lucio Galeati, Fabian A. Harang, Avi Mayorcas
Author Affiliations +
Electron. J. Probab. 27: 1-38 (2022). DOI: 10.1214/22-EJP756


We study distribution dependent stochastic differential equation driven by a continuous process, without any specification on its law, following the approach initiated in [17]. 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.

Funding Statement

FH gratefully acknowledges financial support from the STORM project 274410, funded by the Research Council of Norway. LG is funded by the DFG under Germany’s Excellence Strategy – GZ 2047/1, project-id 390685813.


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Lucio Galeati. Fabian A. Harang. Avi Mayorcas. "Distribution dependent SDEs driven by additive continuous noise." Electron. J. Probab. 27 1 - 38, 2022.


Received: 4 June 2021; Accepted: 11 February 2022; Published: 2022
First available in Project Euclid: 3 March 2022

arXiv: 2105.14056
MathSciNet: MR4388460
zbMATH: 1492.60168
Digital Object Identifier: 10.1214/22-EJP756

Primary: 60F15 , 60H10
Secondary: 34F05 , 60K35

Keywords: Additive Noise , McKean–Vlasov equation , mean field limit , pathwise approach

Vol.27 • 2022
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