Stochastic analysis of external and parametric dynamical systems under sub-Gaussian Lévy white-noise

Massimiliano Zingales, Mario Di Paola, Antonina Pirrotta, Mario Di Paola, Massimiliano Zingales, Antonina Pirrotta

Risultato della ricerca: Article

Abstract

In this study stochastic analysis of non-linear dynamical systems under α-stable,multiplicative white noise has been conducted. The analysis has dealt with a special class of α-stablestochastic processes namely sub-Gaussian white noises. In this setting the governing equation either of theprobability density function or of the characteristic function of the dynamical response may be obtainedconsidering the dynamical system forced by a Gaussian white noise with an uncertain factor with α/2-stable distribution. This consideration yields the probability density function or the characteristic functionof the response by means of a simple integral involving the probability density function of the systemunder Gaussian white noise and the probability density function of the α/2-stable random parameter. Somenumerical applications have been reported assessing the reliability of the proposed formulation. Moreovera proper way to perform digital simulation of the sub-Gaussian α-stable random process preventingdynamical systems from numerical overflows has been reported and discussed in detail.
Lingua originaleEnglish
pagine (da-a)373-386
Numero di pagine13
RivistaStructural Engineering and Mechanics
Volume28
Stato di pubblicazionePublished - 2008

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White noise
Probability density function
Dynamical systems
Nonlinear dynamical systems
Random processes

All Science Journal Classification (ASJC) codes

  • Civil and Structural Engineering
  • Building and Construction
  • Mechanics of Materials
  • Mechanical Engineering

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Stochastic analysis of external and parametric dynamical systems under sub-Gaussian Lévy white-noise. / Zingales, Massimiliano; Di Paola, Mario; Pirrotta, Antonina; Di Paola, Mario; Zingales, Massimiliano; Pirrotta, Antonina.

In: Structural Engineering and Mechanics, Vol. 28, 2008, pag. 373-386.

Risultato della ricerca: Article

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abstract = "In this study stochastic analysis of non-linear dynamical systems under α-stable,multiplicative white noise has been conducted. The analysis has dealt with a special class of α-stablestochastic processes namely sub-Gaussian white noises. In this setting the governing equation either of theprobability density function or of the characteristic function of the dynamical response may be obtainedconsidering the dynamical system forced by a Gaussian white noise with an uncertain factor with α/2-stable distribution. This consideration yields the probability density function or the characteristic functionof the response by means of a simple integral involving the probability density function of the systemunder Gaussian white noise and the probability density function of the α/2-stable random parameter. Somenumerical applications have been reported assessing the reliability of the proposed formulation. Moreovera proper way to perform digital simulation of the sub-Gaussian α-stable random process preventingdynamical systems from numerical overflows has been reported and discussed in detail.",
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AU - Zingales, Massimiliano

AU - Di Paola, Mario

AU - Pirrotta, Antonina

AU - Di Paola, Mario

AU - Zingales, Massimiliano

AU - Pirrotta, Antonina

PY - 2008

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AB - In this study stochastic analysis of non-linear dynamical systems under α-stable,multiplicative white noise has been conducted. The analysis has dealt with a special class of α-stablestochastic processes namely sub-Gaussian white noises. In this setting the governing equation either of theprobability density function or of the characteristic function of the dynamical response may be obtainedconsidering the dynamical system forced by a Gaussian white noise with an uncertain factor with α/2-stable distribution. This consideration yields the probability density function or the characteristic functionof the response by means of a simple integral involving the probability density function of the systemunder Gaussian white noise and the probability density function of the α/2-stable random parameter. Somenumerical applications have been reported assessing the reliability of the proposed formulation. Moreovera proper way to perform digital simulation of the sub-Gaussian α-stable random process preventingdynamical systems from numerical overflows has been reported and discussed in detail.

KW - Fokker-Planck equation

KW - Lévy white noise

KW - stochastic differential calculus

KW - sub-Gaussian white noise.

UR - http://hdl.handle.net/10447/43477

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VL - 28

SP - 373

EP - 386

JO - Structural Engineering and Mechanics

JF - Structural Engineering and Mechanics

SN - 1225-4568

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