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Linear systems with Lévy fluctuations

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  • West, Bruce J.
  • Seshadri, V.

Abstract

We have examined the response of multivariable linear systems to Lévy fluctuations. The characteristic function of the response is obtained explicitly as a function of time. Using the characteristic function, the fractional moments of the process are determined. The nature of the product rule obeyed by the characteristic function of a general linear dynamical system is elucidated.

Suggested Citation

  • West, Bruce J. & Seshadri, V., 1982. "Linear systems with Lévy fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 113(1), pages 203-216.
    • Handle: RePEc:eee:phsmap:v:113:y:1982:i:1:p:203-216
    DOI: 10.1016/0378-4371(82)90015-2
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    Cited by:

    1. Hongler, Max-Olivier & Filliger, Roger & Blanchard, Philippe, 2006. "Soluble models for dynamics driven by a super-diffusive noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(2), pages 301-315.
    2. Gorenflo, Rudolf & Fabritiis, Gianni De & Mainardi, Francesco, 1999. "Discrete random walk models for symmetric Lévy–Feller diffusion processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 269(1), pages 79-89.
    3. Gorenflo, Rudolf & Mainardi, Francesco & Moretti, Daniele & Pagnini, Gianni & Paradisi, Paolo, 2002. "Fractional diffusion: probability distributions and random walk models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 305(1), pages 106-112.
    4. West, Bruce J., 1996. "Lévy statistics of water wave forces," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 230(3), pages 359-363.
    5. Janicki, Aleksander & Weron, Aleksander, 1995. "Computer simulation of attractors in stochastic models with α-stable noise," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 39(1), pages 9-19.
    6. Paradisi, Paolo & Cesari, Rita & Mainardi, Francesco & Tampieri, Francesco, 2001. "The fractional Fick's law for non-local transport processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 293(1), pages 130-142.

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