Symplectic Euler scheme for Hamiltonian stochastic differential equations driven by Levy noise

Abstract

This paper proposes a general symplectic Euler scheme for a class of Hamiltonian stochastic differential equations driven by Lévy noise in the sense of Marcus form. The convergence of the symplectic Euler scheme for this Hamiltonian stochastic differential equations is investigated. Realizable numerical implementation of this scheme is also provided in details. Numerical experiments are presented to illustrate the effectiveness and superiority of the proposed method by the simulations of its orbits, symplectic structure and Hamlitonian.

Numerical integration of stochastic contact Hamiltonian systems via stochastic Herglotz variational principle

“…As the counterpart of contact case, much attention have been paid to stochastic symplectic methods [7][8][9][10][11][12]. As we know, structure-preserving algorithm has been widely applied in many aspects.…”

“…Then it is natural to expect to expand it to the stochastic contact Hamiltonian systems. Second, many contributions have been made to the numerical analysis of SDEs [12,21,22]. The readers can find more information on numerical topic in these references.…”