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
Energy
Multilevel Monte Carlo
Author
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 27Approximation and simulation of Lévy-driven SPDE
Swedish Research Council (VR) (2014-3995), 2015-01-01 -- 2018-12-31.
Subject Categories
Computational Mathematics
Control Engineering
Signal Processing
Roots
Basic sciences
DOI
10.1007/s10444-020-09771-5