Geodesic
The analysis of stability of a linear oscillator with multiplicative noise
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 10 (2007) no. 2, pp. 127-145 
T. A. Averina; A. A. Alifirenko. The analysis of stability of a linear oscillator with multiplicative noise. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 10 (2007) no. 2, pp. 127-145. http://geodesic.mathdoc.fr/item/SJVM_2007_10_2_a1/
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     title = {The analysis of stability of a~linear oscillator with multiplicative noise},
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we investigate a linear SDE of second order in the Ito sense with a multiplicative noise with real parameters. This equation was reduced to a two-dimensional linear SDEs system of first order with the help of replacement of variables. This linear SDEs system is linearization of an arbitrary two-dimensional nonlinear system. We investigate the stability of a trivial solution to a linear system SDE. We obtain conditions for parameters of the system for various modes of stability. We compare the known numerical methods on the solution of an oscillatory system.

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