SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Invited Talk

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A review on numerical schemes for solving a linear stochastic oscillator

M.J. Senosiain and A. Tocino

Abstract
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, namely, symplecticity, linear growth of its second moment and asymptotic oscillation around zero, among others. In this work 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.

Bibliography
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[2] G.N. Milstein, Yu. M. Repin and M. V. Tretyakov, Symplectic integration of Hamiltonian systems with additive noise, SIAM J. Numer. Anal. 39 (2002) 2066-2088.
[3] H. Schurz, New stochastic integrals, oscillation theorems and energy identities, Com. Appl. Analysis 13 (2009), no. 2, pp. 181-194.
[4] A.H. Stømmen and D.J. Higham, Numerical simulation of a linear stochastic oscillator with additive noise, Appl. Numer. Math. 51 (2004), no. 1, pp. 89-99.

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