A new class of symplectic methods for stochastic Hamiltonian systems
Author
Faculty Advisor
Date
2025
Keywords
Stochastic Hamiltonian systems, Stochastic Runge-Kutta methods, generating function, symplectic integration
Abstract (summary)
We propose a systematic approach to construct a new family of stochastic symplectic schemes for the strong approximation of the solution of stochastic Hamiltonian systems. Our approach is based both on B-series and generating functions. The proposed schemes are a generalization of the implicit midpoint rule, they require derivatives of the Hamiltonian functions of at most order two, and are constructed by defining a generating function. We construct some schemes with strong convergence order one and a half, and we illustrate numerically their long term performance.
Publication Information
Anton, C. (2025). A new class of symplectic methods for stochastic Hamiltonian systems. Applied Numerical Mathematics, 208, 43–59. https://doi.org/10.1016/j.apnum.2024.01.021
Notes
Item Type
Article Pre-Print
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Rights
Attribution-NonCommercial-NoDerivs (CC BY-NC-ND)
