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

Mao, X. and Yuan, C. (2008) A note on the rate of convergence of the Euler-Maruyama method for stochastic differential equations. Stochastic Analysis and Applications, 26 (2). pp. 325-333. ISSN 0736-2994

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.

ORCID iDs

Mao, X. ORCID: https://orcid.org/0000-0002-6768-9864

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  Item type:	Article
  ID code:	14042
  Dates:	Date Event 2008 Published
  Keywords:	brownian motion, euler-maruyama method, lipschitz condition, differential equations, Mathematics, Applied Mathematics, Statistics and Probability, Statistics, Probability and Uncertainty
  Subjects:	Science > Mathematics
  Department:	Faculty of Science > Mathematics and Statistics
  Depositing user:	Mrs Carolynne Westwood
  Date deposited:	11 Jan 2010 16:59
  Last modified:	19 Mar 2021 03:48
  URI:	https://strathprints.strath.ac.uk/id/eprint/14042