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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2007, Volume 10, Number 2, Pages 127–145
(Mi sjvm72)
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This article is cited in 1 scientific paper (total in 1 paper)
The analysis of stability of a linear oscillator with multiplicative noise
T. A. Averinaa, A. A. Alifirenkob a 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.
Received: 28.12.2005 Revised: 11.05.2006
Citation:
T. A. Averina, A. A. Alifirenko, “The analysis of stability of a linear oscillator with multiplicative noise”, Sib. Zh. Vychisl. Mat., 10:2 (2007), 127–145
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https://www.mathnet.ru/eng/sjvm72 https://www.mathnet.ru/eng/sjvm/v10/i2/p127
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Abstract page: | 299 | Full-text PDF : | 233 | References: | 35 |
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