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

Author

Listed:
  • Alotta, G.
  • Di Paola, M.

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.

Suggested Citation

  • Alotta, G. & Di Paola, M., 2015. "Probabilistic characterization of nonlinear systems under α-stable white noise via complex fractional moments," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 420(C), pages 265-276.
    • Handle: RePEc:eee:phsmap:v:420:y:2015:i:c:p:265-276
    DOI: 10.1016/j.physa.2014.10.091
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    References listed on IDEAS

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    1. Cottone, Giulio & Di Paola, Mario & Metzler, Ralf, 2010. "Fractional calculus approach to the statistical characterization of random variables and vectors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(5), pages 909-920.
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