4.2 Article

Distribution dependent SDEs driven by additive continuous noise

期刊

ELECTRONIC JOURNAL OF PROBABILITY
卷 27, 期 -, 页码 -

出版社

INST MATHEMATICAL STATISTICS-IMS
DOI: 10.1214/22-EJP756

关键词

additive noise; pathwise approach; McKean-Vlasov equation; mean field limit

资金

  1. Research Council of Norway [274410]
  2. DFG under Germany's Excellence Strategy [GZ 2047/1, 390685813]

向作者/读者索取更多资源

This article studies distribution dependent stochastic differential equation driven by a continuous process, without any specification on its law, following the approach initiated in [17]. Several criteria for existence and uniqueness of solutions beyond the classical globally Lipschitz setting are provided. In particular, well-posedness of the equation and almost sure convergence of the associated particle system are shown for drifts satisfying either Osgood-continuity, monotonicity, local Lipschitz or Sobolev differentiability type assumptions.
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.

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