A third-order weak approximation of multidimensional Itô stochastic differential equations. (English) Zbl 1418.60101
Summary: This paper proposes a new third-order discretization algorithm for multidimensional Itô stochastic differential equations driven by Brownian motions. The scheme is constructed by the Euler-Maruyama scheme with a stochastic weight given by polynomials of Brownian motions, which is simply implemented by a Monte Carlo method. The method of Watanabe distributions on Wiener space is effectively applied in the computation of the polynomial weight of Brownian motions. Numerical examples are shown to confirm the accuracy of the scheme.
MSC:
| 60H35 | Computational methods for stochastic equations (aspects of stochastic analysis) |
| 65C05 | Monte Carlo methods |
| 65C30 | Numerical solutions to stochastic differential and integral equations |
| 91G60 | Numerical methods (including Monte Carlo methods) |
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