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Models of anomalous diffusion: the subdiffusive case

  • Piryatinska, A.
  • Saichev, A.I.
  • Woyczynski, W.A.
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    The paper discusses a model for anomalous diffusion processes. Their one-point probability density functions (p.d.f.) are exact solutions of fractional diffusion equations. The model reflects the asymptotic behavior of a jump (anomalous random walk) process with random jump sizes and random inter-jump time intervals with infinite means (and variances) which do not satisfy the Law of Large Numbers. In the case when these intervals have a fractional exponential p.d.f., the fractional Komogorov–Feller equation for the corresponding anomalous diffusion is provided and methods of finding its solutions are discussed. Finally, some statistical properties of solutions of the related Langevin equation are studied. The subdiffusive case is explored in detail.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0378437104014098
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    Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

    Volume (Year): 349 (2005)
    Issue (Month): 3 ()
    Pages: 375-420

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    Handle: RePEc:eee:phsmap:v:349:y:2005:i:3:p:375-420
    Contact details of provider: Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

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    1. Mann Jr, J.A. & Woyczynski, W.A., 2001. "Growing fractal interfaces in the presence of self-similar hopping surface diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 291(1), pages 159-183.
    2. Enrico Scalas & Rudolf Gorenflo & Francesco Mainardi, 2004. "Fractional calculus and continuous-time finance," Finance 0411007, EconWPA.
    3. Mainardi, Francesco & Raberto, Marco & Gorenflo, Rudolf & Scalas, Enrico, 2000. "Fractional calculus and continuous-time finance II: the waiting-time distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 468-481.
    4. Bazzani, Armando & Bassi, Gabriele & Turchetti, Giorgio, 2003. "Diffusion and memory effects for stochastic processes and fractional Langevin equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(3), pages 530-550.
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