Strong Solutions of Mean-Field Stochastic Differential Equations with\n irregular drift

2018/06/29 by Martin Bauer, Bauer, Martin, Thilo Meyer‐Brandis +3 · 1 citation
Economics, Econometrics and Finance · Mathematics · Social Sciences · #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Probability (math.PR) #Statistical Methods and Inference #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1806.11451

openalex publication_date 2018/06/29 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

We investigate existence and uniqueness of strong solutions of mean-field\nstochastic differential equations with irregular drift coefficients. Our direct\nconstruction of strong solutions is mainly based on a compactness criterion\nemploying Malliavin Calculus together with some local time calculus.\nFurthermore, we establish regularity properties of the solutions such as\nMalliavin differentiablility as well as Sobolev differentiability in the\ninitial condition. Using this properties we formulate an extension of the\nBismut-Elworthy-Li formula to mean-field stochastic differential equations to\nget a probabilistic representation of the first order derivative of an\nexpectation functional with respect to the initial condition.\n

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