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Media type:
E-Book
Title:
Numerical schemes for the long-term simulation of SDE's with additive noise and their effectiveness in the integration of a stochastic oscillator
Description:
We propose and analyze numerical methods for the long-term integration of stochastic differential equations (SDEs) with additive noise. By focusing on a linear stochastic oscillator as a test equation, it is shown that these methods are able to reproduce key features related to the long term behavior of this system: they mimic the linear growth of the second moment of the solution, an infinitely-oscillation property and the symplectic structure of this Hamiltonian system. We show the advantages over long periods of time of the proposed integrators in comparison with commonly-used methods for the integration of SDEs. The theoretical findings are illustrated by computer experiments.