Strong convergence of Euler-Maruyama schemes for McKean-Vlasov stochastic differential equations under local Lipschitz conditions of state variables

Yun Li, Xuerong Mao, Qingshuo Song, Fuke Wu, George Yin

Research output: Contribution to journalArticlepeer-review

Abstract

This paper develops strong convergence of the Euler-Maruyama (EM) schemes for approximating McKean-Vlasov stochastic differential equations (SDEs). In contrast to the existing work, a novel feature is the use of a much weaker condition-local Lipschitzian in the state variable but under uniform linear growth assumption. To obtain the desired approximation, the paper first establishes the existence and uniqueness of solutions of the original McKean-Vlasov SDE using an Euler-like sequence of interpolations and partition of the sample space. Then, the paper returns to the analysis of the EM scheme for approximating solutions of McKean-Vlasov SDEs. A strong convergence theorem is established. Moreover, the convergence rates under global conditions are obtained.
Original languageEnglish
JournalIMA Journal of Numerical Analysis
Early online date31 Jan 2022
DOIs
Publication statusE-pub ahead of print - 31 Jan 2022

Keywords

  • McKean-Vlasov SDE
  • one-sided local Lipschitz condition
  • local Lipschitz condition
  • interpolated Euler-like sequence
  • Euler-Maruyama scheme

Cite this