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First-order convergence of Milstein schemes for McKean-Vlasov equations and interacting particle systems.

ABSTRACT: In this paper, we derive fully implementable first-order time-stepping schemes for McKean-Vlasov stochastic differential equations, allowing for a drift term with super-linear growth in the state component. We propose Milstein schemes for a time-discretized interacting particle system associated with the McKean-Vlasov equation and prove strong convergence of order 1 and moment stability, taming the drift if only a one-sided Lipschitz condition holds. To derive our main results on strong convergence rates, we make use of calculus on the space of probability measures with finite second-order moments. In addition, numerical examples are presented which support our theoretical findings.

SUBMITTER: Bao J

PROVIDER: S-EPMC7897642 | biostudies-literature |

REPOSITORIES: biostudies-literature

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