Generating functions for stochastic symplectic methods

Lijin Wang; Jialin Hong

doi:10.3934/dcds.2014.34.1211

Article Contents

2014, Volume 34, Issue 3: 1211-1228. Doi: 10.3934/dcds.2014.34.1211

This issue Previous Article The Landau--Kolmogorov inequality revisited Next Article Generating functions and volume preserving mappings

Generating functions for stochastic symplectic methods

Lijin Wang^1, and
Jialin Hong^2,

1.
School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049
2.
State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190

Received: October 31, 2012

Revised: March 31, 2013

Published: February 2014

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Abstract

Symplectic integration of stochastic Hamiltonian systems is a developing branch of stochastic numerical analysis. In the present paper, a stochastic generating function approach is proposed, based on the derivation of stochastic Hamilton-Jacobi PDEs satisfied by the generating functions, and a method of approximating solutions to them. Thus, a systematic approach of constructing stochastic symplectic methods is provided. As validation, numerical tests on several stochastic Hamiltonian systems are performed, where some symplectic schemes are constructed via stochastic generating functions. Moreover, generating functions for some known stochastic symplectic mappings are given.

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Mathematics Subject Classification: 65P10, 65C30, 65C20, 65H10.

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