Journal Article

STRONG CONVERGENCE OF AN EXPLICIT NUMERICAL METHOD FOR SDES WITH NONGLOBALLY LIPSCHITZ CONTINUOUS COEFFICIENTS

Hutzenthaler, Martin, Kloeden, Peter E., Jentzen, Arnulf

2012

Overview

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.

• Publisher: Institute of Mathematical Statistics,The Institute of Mathematical Statistics
• Subject: 65C30 / Approximation / Backward Euler scheme / Coefficients / Convergence / Differential equations / Error rates / Euler scheme / Eulers equations / Eulers method / Euler–Maruyama / implicit Euler scheme / nonglobally Lipschitz / Numerical analysis / Numerical methods / Perceptron convergence procedure / Platens / Roots of functions / Simulation / stochastic differential equation / Stochastic models / Stochastic processes / strong approximation / superlinearly growing coefficient / tamed Euler scheme