Foundations of Computational Mathematics

, Volume 11, Issue 6, pp 657–706 | Cite as

Convergence of the Stochastic Euler Scheme for Locally Lipschitz Coefficients

Article

Abstract

Stochastic differential equations are often simulated with the Monte Carlo Euler method. Convergence of this method is well understood in the case of globally Lipschitz continuous coefficients of the stochastic differential equation. However, the important case of superlinearly growing coefficients has remained an open question. The main difficulty is that numerically weak convergence fails to hold in many cases of superlinearly growing coefficients. In this paper we overcome this difficulty and establish convergence of the Monte Carlo Euler method for a large class of one-dimensional stochastic differential equations whose drift functions have at most polynomial growth.

Keywords

Euler scheme Stochastic differential equations Monte Carlo Euler method Local Lipschitz condition 

Mathematics Subject Classification (2000)

65C05 60H35 65C30 

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Copyright information

© SFoCM 2011

Authors and Affiliations

  1. 1.LMU Biozentrum, Department Biologie IIUniversity of Munich (LMU)Planegg-MartinsriedGermany
  2. 2.Program in Applied and Computational MathematicsPrinceton UniversityPrincetonUSA

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