Drift-preserving numerical integrators for stochastic Hamiltonian systems
Journal article, 2020

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

Strong convergence

Numerical schemes

Weak convergence

Stochastic differential equations

Stochastic Hamiltonian systems


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

Advances in Computational Mathematics

1019-7168 (ISSN) 1572-9044 (eISSN)

Vol. 46 2

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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2/5/2021 4