论文信息 - Weak Second Order Conditions for Stochastic Runge-Kutta Methods

Weak Second Order Conditions for Stochastic Runge-Kutta Methods

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.

Jesús Vigo-Aguiar | A. Tocino | J. Vigo-Aguiar | Á. Tocino

[1] J. Vigo-Aguiar,et al. An Infinite Family of Second Order Weak Explicit Runge-Kutta Methods , 2001 .

[2] Denis Talay,et al. Efficient numerical schemes for the approximation of expectations of functionals of the solution of a S.D.E., and applications , 1984 .

[3] A. Tocino,et al. Truncated ITÔ-Taylor expansions , 2002 .

[4] P. Kloeden,et al. Numerical Solution of Stochastic Differential Equations , 1992 .

[5] J. Lambert. Numerical Methods for Ordinary Differential Systems: The Initial Value Problem , 1991 .

[6] B. Øksendal. Stochastic Differential Equations , 1985 .

[7] S. Shreve,et al. Stochastic differential equations , 1955, Mathematical Proceedings of the Cambridge Philosophical Society.

[8] G. Mil’shtein. Weak Approximation of Solutions of Systems of Stochastic Differential Equations , 1986 .

[9] R. Ardanuy,et al. Runge-Kutta methods for numerical solution of stochastic differential equations , 2002 .

[10] E. Platen. An introduction to numerical methods for stochastic differential equations , 1999, Acta Numerica.

[11] G. Mil’shtein. A Method of Second-Order Accuracy Integration of Stochastic Differential Equations , 1979 .