Approximations of Mckean-Vlasov SDEs with Irregular Coefficients

Abstract

The goal of this paper is to approximate several kinds of {\it Mckean-Vlasov SDEs} with {\it irregular coefficients} via weakly interacting particle systems. More precisely, propagation of chaos and convergence rate of Euler-Maruyama scheme associated with the consequent weakly interacting particle systems are investigated for Mckean-Vlasov SDEs, where (i) the diffusion terms are Hölder continuous by taking advantage of Yamada-Watanabe's approximation approach and (ii) the drifts are Hölder continuous by freezing distributions followed by invoking Zvonkin's transformation trick.

arXiv comment19 pages

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Cited by in corpus (5)

• Well-posedness and numerical schemes for one-dimensional McKean-Vlasov equations and interacting particle systems with discontinuous drift
• A discretized version of Krylov's estimate and its applications
• Long-time behaviour for distribution dependent SDEs with local Lipschitz coefficients
• Some remarks on the effect of the Random Batch Method on phase transition
• Explicit Numerical Approximations for McKean-Vlasov Neutral Stochastic Differential Delay Equations