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

By Martin Bauer, T. Meyer‐Brandis, Frank Norbert Proske. 2018

65 citations recorded by the source corpus.

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 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.

Subfields: Demography, Finance

View Paper: https://www.semanticscholar.org/paper/d6a696116117c240a23c633b5fb598757a0e8e40

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Citations in the corpus

Distribution dependent SDEs driven by additive fractional Brownian motion (2021, methodology): “The latter topic was initiated by Zvonkin [47] and Veretennikov [45] in the case of standard SDEs, see [13] for a general overview; recently many authors have applied similar techniques in the DDSDE case, see for instance [5, 33, 38, 11, 24].”
Mckean-Vlasov sdes with drifts discontinuous under wasserstein distance (2020, background): “Recently, the (weak and strong) well-posedness is studied in [3, 4, 6, 13, 17, 18, 20] for (1) with σt(x, γ) = σt(x) independent of the distribution variable γ, and with singular drift bt(x, γ).”