Weak Second Order Conditions for Stochastic Runge--Kutta Methods

Authors:
A. Tocino;J. Vigo-Aguiar
Affiliations:
-;-
Venue:
SIAM Journal on Scientific Computing
Year:
2002

Citing 0
Cited 18

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Abstract

A general procedure to construct weak methods for the numerical solution of stochastic differential systems is presented. As in the deterministic case, the procedure consists of comparing the stochastic expansion of the approximation with the corresponding Taylor scheme. In this way the authors obtain the order conditions that a stochastic Runge--Kutta method must satisfy to have weak order two. Explicit examples of generalizations of the classical family of second order two-stage explicit Runge--Kutta methods are shown. Also numerical examples are presented.