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

Bauer, Martin; Meyer-Brandis, Thilo and Proske, Frank (2018): Strong solutions of mean-field stochastic differential equations with irregular drift. In: Electronic Journal of Probability, Vol. 23, 132

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 Holder 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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics; Mathematics, Computer Science and Statistics > Mathematics > Workgroup Financial Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 1083-6489
• Language: English