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Damped vibrations excited by white noise

Published online by Cambridge University Press:  01 July 2016

Enzo Orsingher
Enzo Orsingher*
Affiliation:
University of Rome
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Abstract

Let v(x, t) denote the displacement of an infinitely long, idealized string performing damped vibrations caused by white noise.

Upper and lower bounds for the distribution of maxsv(x, s) and maxxv(x, t) are presented. The results are obtained by adapting Lévy-type inequalities and exploiting a connection of v(x, t) with the Ornstein-Uhlenbeck process through Slepian's theorem.

The case of forced-damped vibrations is also analysed. Finally, a section is devoted to the case of a semi-infinite string performing damped vibrations.

Keywords

ORNSTEIN-UHLENBECK PROCESSLÉVY-TYPE INEQUALITIESBROWNIAN MOTIONGREEN'S FUNCTION
Type
Research Article
Information
Advances in Applied Probability , Volume 16 , Issue 3 , September 1984 , pp. 562 - 584
Copyright
Copyright © Applied Probability Trust 1984 

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References

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