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Stochastic models of damped vibrations

Part of: Stochastic processes Stochastic analysis

Published online by Cambridge University Press:  14 July 2016

Maged Elshamy
Maged Elshamy*
Affiliation:
Alabama A&M University
*
∗Postal address: Department of Mathematics, Alabama A&M University, P.O. Box 326, Normal, Alabama 35762, USA.
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Abstract

In this article we study stochastic perturbations of partial differential equations describing forced-damped vibrations of a string. Two models of such stochastic disturbances are considered; one is triggered by an initial white noise, and the other is in the form of non-Gaussian random forcing. Let uε (t, x) be the displacement at time t of a point x on a string, where the time variable t ≧ 0, and the space variable . The small parameter ε controls the intensity of the random fluctuations. The random fields uε (t, x) are shown to satisfy a large deviations principle, and the random deviations of the unperturbed displacement function are analyzed as the noise parameter ε tends to zero.

Keywords

STOCHASTIC PERTURBATIONSDAMPED VIBRATIONSBROWNIAN SHEETRANDOM FIELDSDEVIATIONS

MSC classification

Primary: 60H15: Stochastic partial differential equations 60G60: Random fields
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 4 , December 1996 , pp. 1159 - 1168
Copyright
Copyright © Applied Probability Trust 1996 

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References

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