caa a22 4500 605497257 CHVBK 20210128100540.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s10543-014-0507-z doi (NATIONALLICENCE)springer-10.1007/s10543-014-0507-z A review on numerical schemes for solving a linear stochastic oscillator [Elektronische Daten] [M. Senosiain, A. Tocino] In recent years several numerical methods to solve a linear stochastic oscillator with one additive noise have been proposed. The usual aim of these approaches was to preserve different long time properties of the oscillator solution. In this work we collect these properties, namely, symplecticity, linear growth of its second moment and asymptotic oscillation around zero. We show that these features can be studied in terms of the coefficients of the matrices that appear in the linear recurrence obtained when the schemes are applied to the oscillator. We use this study to compare the numerical schemes as well as to propose new schemes improving some properties of classical methods. Springer Science+Business Media Dordrecht, 2014 Stochastic differential equations nationallicence Stochastic oscillator nationallicence Stochastic Hamiltonian systems nationallicence Stochastic numerical methods nationallicence Stochastic symplectic integrators nationallicence Second order moment nationallicence Senosiain M. Department of Mathematics, University of Salamanca, Salamanca, Spain aut Tocino A. Department of Mathematics, University of Salamanca, Salamanca, Spain aut BIT Numerical Mathematics Springer Netherlands 55/2(2015-06-01), 515-529 0006-3835 55:2<515 2015 55 10543 https://doi.org/10.1007/s10543-014-0507-z text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10543-014-0507-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Senosiain M. Department of Mathematics, University of Salamanca, Salamanca, Spain aut NATIONALLICENCE 700 1- Tocino A. Department of Mathematics, University of Salamanca, Salamanca, Spain aut NATIONALLICENCE 773 0- BIT Numerical Mathematics Springer Netherlands 55/2(2015-06-01), 515-529 0006-3835 55:2<515 2015 55 10543