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- W2900346274 abstract "We discuss the behavior, for large values of time, of a class of linear mechanical systems with a multiplicative white noise in its parameters. The initial conditions may be random as well but are independent of white noise. It is well known that a deterministic linear mechanical system with viscous damping is stable, i.e., its energy approaches zero as time increases. We calculate the expected energy and check that this behavior takes place in the case when the initial conditions are random but the parameters are not. When the parameters contain a random noise the expected energy may be infinite, approach zero, remain bounded, or increase with no bound. We give necessary and sufficient conditions for stability of the systems considered in terms of the roots of an auxiliary equation." @default.
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- W2900346274 date "2003-04-01" @default.
- W2900346274 modified "2023-09-26" @default.
- W2900346274 title "Stochastic stability of some mechanical systems with a multiplicative white noise" @default.
- W2900346274 doi "https://doi.org/10.3934/proc.2003.2003.91" @default.
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