Strong backward error analysis of symplectic integrators for stochastic Hamiltonian systems. (English) Zbl 07834031
Summary: Backward error analysis is a powerful tool in order to detect the long-term conservative behavior of numerical methods. In this work, we present a long-term analysis of symplectic stochastic numerical integrators, applied to Hamiltonian systems with multiplicative noise. We first compute and analyze the associated stochastic modified differential equations. Then, suitable bounds for the coefficients of such equations are provided towards the computation of long-term estimates for the Hamiltonian deviations occurring along the aforementioned numerical dynamics. This result generalizes Benettin-Giorgilli Theorem to the scenario of stochastic symplectic methods. Finally, specific numerical methods are considered, in order to provide a numerical evidence confirming the effectiveness of the theoretical investigation.
MSC:
| 65C30 | Numerical solutions to stochastic differential and integral equations |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 65L07 | Numerical investigation of stability of solutions to ordinary differential equations |
Keywords:
stochastic Hamiltonian systems; modified differential equations; symplectic methods; strong backward error analysisSoftware:
LIMbookReferences:
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