Articlegold2018

Strong solutions of mean-field stochastic differential equations with irregular drift

47 citations0/0 files storedElectronic Journal of Probability

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Stochastic processes and financial applications Nonlinear Differential Equations Analysis Fuzzy Systems and Optimization

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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References

2007Mean field games 2008Malliavin Calculus for Lévy Processes with Applications to Finance 2013Probabilistic Analysis of Mean-Field Games 2009Mean-field backward stochastic differential equations and related partial differential equations 2009Mean-field backward stochastic differential equations: A limit approach 2017Mean-field stochastic differential equations and associated PDEs 2015Mean Field Games and systemic risk 2015Forward–backward stochastic differential equations and controlled McKean–Vlasov dynamics

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