Transient behaviour of semilinear stochastic systems with random parameters.

*(English)*Zbl 0532.93050The 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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