The Annals of Applied Probability

Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients

Martin Hutzenthaler, Arnulf Jentzen, and Peter E. Kloeden

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Abstract

On the one hand, the explicit Euler scheme fails to converge strongly to the exact solution of a stochastic differential equation (SDE) with a superlinearly growing and globally one-sided Lipschitz continuous drift coefficient. On the other hand, the implicit Euler scheme is known to converge strongly to the exact solution of such an SDE. Implementations of the implicit Euler scheme, however, require additional computational effort. In this article we therefore propose an explicit and easily implementable numerical method for such an SDE and show that this method converges strongly with the standard order one-half to the exact solution of the SDE. Simulations reveal that this explicit strongly convergent numerical scheme is considerably faster than the implicit Euler scheme.

Article information

Source
Ann. Appl. Probab. Volume 22, Number 4 (2012), 1611-1641.

Dates
First available in Project Euclid: 10 August 2012

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1344614205

Digital Object Identifier
doi:10.1214/11-AAP803

Mathematical Reviews number (MathSciNet)
MR2985171

Zentralblatt MATH identifier
1256.65003

Subjects
Primary: 65C30: Stochastic differential and integral equations

Keywords
Euler scheme Euler–Maruyama stochastic differential equation strong approximation tamed Euler scheme implicit Euler scheme Backward Euler scheme nonglobally Lipschitz superlinearly growing coefficient

Citation

Hutzenthaler, Martin; Jentzen, Arnulf; Kloeden, Peter E. Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients. Ann. Appl. Probab. 22 (2012), no. 4, 1611--1641. doi:10.1214/11-AAP803. https://projecteuclid.org/euclid.aoap/1344614205.


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