Volume 43, pp. 1-20, 2014-2015.

Weak symplectic schemes for stochastic Hamiltonian equations

Cristina Anton, Jian Deng, and Yau Shu Wong

Abstract

We propose a systematic approach to construct symplectic schemes in the weak sense for stochastic Hamiltonian systems. This method is based on generating functions, so it is an extension of the techniques used for constructing high-order symplectic schemes for deterministic Hamiltonian systems. Although the developed symplectic schemes are implicit, they are comparable with the explicit weak Taylor schemes in terms of the number and the complexity of the multiple Itô stochastic integrals required. We study the convergence of the proposed symplectic weak order 2 schemes. The excellent long term performance of the symplectic schemes is verified numerically.

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Key words

stochastic Hamiltonian systems, symplectic integration, numerical scheme in weak sense

AMS subject classifications

65C30, 65P10, 60H10

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