Drift-preserving numerical integrators for stochastic Hamiltonian systems

Abstract

The paper deals with numerical discretizations of separable nonlinear Hamiltonian systems with additive noise. For such problems, the expected value of the total energy, along the exact solution, drifts linearly with time. We present and analyze a time integrator having the same property for all times. Furthermore, strong and weak convergence of the numerical scheme along with efficient multilevel Monte Carlo estimators are studied. Finally, extensive numerical experiments illustrate the performance of the proposed numerical scheme.

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Cited by in corpus (4)

• Drift-preserving numerical integrators for stochastic Hamiltonian systems
• Mean-square contractivity of stochastic $\theta$-methods
• Drift-preserving numerical integrators for stochastic Poisson systems
• A dynamic domain semi-Lagrangian method for stochastic Vlasov equations