In this study stochastic analysis of nonlinear dynamical systems under a-stable, multiplicative white noise has been performed. Analysis has been conducted by means of the Itoˆ rule extended to the case of α-stable noises. In this context the order of increments of Levy process has been evaluated and differential equations ruling the evolutions of statistical moments of either parametrically and external dynamical systems have been obtained. The extended Itoˆ rule has also been used to yield the differential equation ruling the evolution of the characteristic function for parametrically excited dynamical systems. The Fourier transform of the characteristic function, namely the probability density function is ruled by the extended Einstein-Smoluchowsky differential equation to case of parametrically excited dynamical systems. Some numerical applications have been reported to assess the reliability of the proposed formulation.
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ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
September 24–28, 2005
Long Beach, California, USA
Conference Sponsors:
- Design Engineering Division and Computers and Information in Engineering Division
ISBN:
0-7918-4738-1
PROCEEDINGS PAPER
Non-Linear Systems Under Parametric Alpha-Stable Le´vy White Noises Available to Purchase
Mario Di Paola,
Mario Di Paola
University of Palermo, Palermo, Italy
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Antonina Pirrotta,
Antonina Pirrotta
University of Palermo, Palermo, Italy
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Massimiliano Zingales
Massimiliano Zingales
University of Palermo, Palermo, Italy
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Mario Di Paola
University of Palermo, Palermo, Italy
Antonina Pirrotta
University of Palermo, Palermo, Italy
Massimiliano Zingales
University of Palermo, Palermo, Italy
Paper No:
DETC2005-85685, pp. 1783-1789; 7 pages
Published Online:
June 11, 2008
Citation
Di Paola, M, Pirrotta, A, & Zingales, M. "Non-Linear Systems Under Parametric Alpha-Stable Le´vy White Noises." Proceedings of the ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 1: 20th Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C. Long Beach, California, USA. September 24–28, 2005. pp. 1783-1789. ASME. https://doi.org/10.1115/DETC2005-85685
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