# American Institute of Mathematical Sciences

March  2014, 34(3): 1211-1228. doi: 10.3934/dcds.2014.34.1211

## Generating functions for stochastic symplectic methods

 1 School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China 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  November 2012 Revised  April 2013 Published  August 2013

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.
Citation: Lijin Wang, Jialin Hong. Generating functions for stochastic symplectic methods. Discrete & Continuous Dynamical Systems - A, 2014, 34 (3) : 1211-1228. doi: 10.3934/dcds.2014.34.1211
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