A note on the rate of convergence of the Euler-Maruyama method for stochastic differential equations

X. Mao, C. Yuan

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

The recent article [2] reveals the strong convergence of the Euler-Maruyama solution to the exact solution of a stochastic differential equation under the local Lipschitz condition. However, it does not provide us with an order of convergence. In this note, we will show the rate of convergence still under the local Lipschitz condition, but the local Lipschitz constants of the drift coefficient, valid on balls of radius R, are supposed not to grow faster than log R while those of the diffusion coefficient are not than.
Original languageEnglish
Pages (from-to)325-333
Number of pages8
JournalStochastic Analysis and Applications
Volume26
Issue number2
DOIs
Publication statusPublished - 2008

Keywords

  • brownian motion
  • euler-maruyama method
  • lipschitz condition
  • differential equations

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