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arXiv · 2105.14056

Distribution dependent SDEs driven by additive continuous noise

Lucio Galeati·Fabian A. Harang·Avi Mayorcas
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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.

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Lucio Galeati, Fabian A. Harang, Avi Mayorcas. 2021-05-28. Distribution dependent SDEs driven by additive continuous noise. https://doi.org/10.1214/22-ejp756

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