Probabilistic characterization of nonlinear systems under α-stable white noise via complex fractional moments

G. Alotta and M. Di Paola

Physica A: Statistical Mechanics and its Applications, 2015, vol. 420, issue C, 265-276

Abstract: The probability density function of the response of a nonlinear system under external α-stable Lévy white noise is ruled by the so called Fractional Fokker–Planck equation. In such equation the diffusive term is the Riesz fractional derivative of the probability density function of the response. The paper deals with the solution of such equation by using the complex fractional moments. The analysis is performed in terms of probability density for a linear and a non-linear half oscillator forced by Lévy white noise with different stability indexes α. Numerical results are reported for a wide range of non-linearity of the mechanical system and stability index of the Lévy white noise.

Keywords: α-stable white noise; Nonlinear systems; Fractional Fokker–Planck equation; Complex fractional moments (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:420:y:2015:i:c:p:265-276

DOI: 10.1016/j.physa.2014.10.091

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