This article is cited in 1 paper

The analysis of stability of a linear oscillator with multiplicative noise

T. A. Averina^a, A. A. Alifirenko<sup>b

a</sup> Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences
^b Novosibirsk State University

Abstract: 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.

Key words: stochastic differential equations (SDEs), linear oscillator, stability of trivial solution, numerical methods for SDEs.

UDC: 519.676

Received: 28.12.2005
Revised: 11.05.2006