Stochastic models of damped vibrations

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...

Full description

Saved in:
Bibliographic Details
Published in:Journal of applied probability 1996-12, Vol.33 (4), p.1159-1168
Main Author: Elshamy, Maged
Format: Article
Language:English
Subjects:
Continuous functions
Determinism
Exact sciences and technology
Mathematics
Partial differential equations
Position function
Probability and statistics
Probability theory and stochastic processes
Random variables
Random vibration
Research Papers
Sciences and techniques of general use
Stochastic analysis
Stochastic models
Stochastic processes
Studies
Vibration
Wave equations
White noise
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0021-9002
1475-6072
DOI:10.2307/3214993