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Transient behaviour of semilinear stochastic systems with random parameters. (English) Zbl 0532.93050
The author deals with a system governed by an n-dimensional evolution equation consisting of three terms: (1) a linear deterministic term with a time-invariant matrix coefficient, (2) a dynamic deterministic term which evolves periodically, (3) a nonlinear deterministic term depending on random parameters whose effects are rapidly absorbed by a small deterministic parameter. Initial random conditions with time-invariant probability density are considered. Within a stochastic operator framework developed by Adomian the author derives analytically approximated expressions for the first- and second-order moments of the system dynamics which are supposed to determine the probability density of the solution of the dynamics, i.e. the evolution equation described above. An application to the stochastic oscillator with a vanishing quadratic nonlinearity is given.
Reviewer: G.Gomez

MSC:
93E03 Stochastic systems in control theory (general)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H25 Random operators and equations (aspects of stochastic analysis)
93E10 Estimation and detection in stochastic control theory
93E12 Identification in stochastic control theory
93E25 Computational methods in stochastic control (MSC2010)
93C10 Nonlinear systems in control theory
70K50 Bifurcations and instability for nonlinear problems in mechanics
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References:
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