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May 2021 Well-posedness of distribution dependent SDEs with singular drifts
Michael Röckner, Xicheng Zhang
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Bernoulli 27(2): 1131-1158 (May 2021). DOI: 10.3150/20-BEJ1268

Abstract

Consider the following distribution dependent SDE:

dXt=σt(Xt,μXt)dWt+bt(Xt,μXt)dt,

where μXt stands for the distribution of Xt. In this paper for non-degenerate σ, we show the strong well-posedness of the above SDE under some integrability assumptions in the spatial variable and Lipschitz continuity in μ about b and σ. In particular, we extend the results of Krylov–Röckner (Probab. Theory Related Fields 131 (2005) 154–196) to the distribution dependent case.

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Michael Röckner. Xicheng Zhang. "Well-posedness of distribution dependent SDEs with singular drifts." Bernoulli 27 (2) 1131 - 1158, May 2021. https://doi.org/10.3150/20-BEJ1268

Information

Received: 1 October 2019; Revised: 1 April 2020; Published: May 2021
First available in Project Euclid: 24 March 2021

Digital Object Identifier: 10.3150/20-BEJ1268

Keywords: Distribution dependent SDEs , McKean–Vlasov system , singular drifts , superposition principle , Zvonkin’s transformation

Rights: Copyright © 2021 ISI/BS

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Vol.27 • No. 2 • May 2021
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