Drift-preserving numerical integrators for stochastic Hamiltonian systems
Preprint, 2019

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.

Trace formula

Weak convergence

Strong convergence

Stochastic Hamiltonian systems

Numerical schemes

Stochastic differential equations


Multilevel Monte Carlo


Chuchu Chen

Chinese Academy of Sciences

David Cohen

Umeå University

Raffaele D'Ambrosio

University of L'Aquila

Annika Lang

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Approximation and simulation of Lévy-driven SPDE

Swedish Research Council (VR), 2015-01-01 -- 2018-12-31.

Subject Categories

Computational Mathematics

Control Engineering

Signal Processing


Basic sciences

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