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2018 Strong solutions of mean-field stochastic differential equations with irregular drift
Martin Bauer, Thilo Meyer-Brandis, Frank Proske
Electron. J. Probab. 23: 1-35 (2018). DOI: 10.1214/18-EJP259

Abstract

We investigate existence and uniqueness of strong solutions of mean-field stochastic differential equations with irregular drift coefficients. Our direct construction of strong solutions is mainly based on a compactness criterion employing Malliavin Calculus together with some local time calculus. Furthermore, we establish regularity properties of the solutions such as Malliavin differentiablility as well as Sobolev differentiability and Hölder continuity in the initial condition. Using this properties we formulate an extension of the Bismut-Elworthy-Li formula to mean-field stochastic differential equations to get a probabilistic representation of the first order derivative of an expectation functional with respect to the initial condition.

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Martin Bauer. Thilo Meyer-Brandis. Frank Proske. "Strong solutions of mean-field stochastic differential equations with irregular drift." Electron. J. Probab. 23 1 - 35, 2018. https://doi.org/10.1214/18-EJP259

Information

Received: 5 July 2018; Accepted: 13 December 2018; Published: 2018
First available in Project Euclid: 22 December 2018

zbMATH: 07021688
MathSciNet: MR3896869
Digital Object Identifier: 10.1214/18-EJP259

Subjects:
Primary: 60H07, 60H10, 60H20, 60H30

JOURNAL ARTICLE
35 PAGES


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