A new class of symplectic methods for stochastic Hamiltonian systems - Anton, Cristina (My University, 2025)
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.
Keywords: Stochastic Hamiltonian systems; Stochastic Runge-Kutta methods; generating function; symplectic integration