On Explicit Milstein-type Scheme for Mckean-Vlasov Stochastic Differential Equations with Super-linear Drift Coefficient

Abstract

We develop an explicit Milstein-type scheme for McKean-Vlasov stochastic differential equations using the notion of derivative with respect to measure introduced by Lions and discussed in \cite{cardaliaguet2013}. The drift coefficient is allowed to grow super-linearly in the space variable. Further, both drift and diffusion coefficients are assumed to be only once differentiable in variables corresponding to space and measure. The rate of strong convergence is shown to be equal to $1.0$ without using Itô's formula for functions depending on measure. The challenges arising due to the dependence of coefficients on measure are tackled and our findings are consistent with the analogous results for stochastic differential equations.

35 pages

References in corpus (2)

• First order convergence of Milstein schemes for McKean-Vlasov equations and interacting particle systems
• Well-posedness and tamed Euler schemes for McKean-Vlasov equations driven by Lévy noise

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• Well-posedness and numerical schemes for one-dimensional McKean-Vlasov equations and interacting particle systems with discontinuous drift
• Full history recursive multilevel Picard approximations for ordinary differential equations with expectations