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Discrete random walk models for symmetric Lévy–Feller diffusion processes

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  • Gorenflo, Rudolf
  • Fabritiis, Gianni De
  • Mainardi, Francesco

Abstract

We propose a variety of models of random walk, discrete in space and time, suitable for simulating stable random variables of arbitrary index α (0<α⩽2), in the symmetric case. We show that by properly scaled transition to vanishing space and time steps our random walk models converge to the corresponding continuous Markovian stochastic processes which we refer to as Lévy–Feller diffusion processes.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:269:y:1999:i:1:p:79-89
    DOI: 10.1016/S0378-4371(99)00082-5
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. 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.
    2. Silvia Vitali & Iva Budimir & Claudio Runfola & Gastone Castellani, 2019. "The Role of the Central Limit Theorem in the Heterogeneous Ensemble of Brownian Particles Approach," Mathematics, MDPI, vol. 7(12), pages 1-9, November.
    3. 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.
    4. Agarwal, Ritu & Kritika, & Purohit, Sunil Dutt, 2021. "Mathematical model pertaining to the effect of buffer over cytosolic calcium concentration distribution," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).

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