Models of anomalous diffusion: the subdiffusive case
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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Volume (Year): 349 (2005)
Issue (Month): 3 ()
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- Scalas, Enrico & Gorenflo, Rudolf & Mainardi, Francesco, 2000.
"Fractional calculus and continuous-time finance,"
Physica A: Statistical Mechanics and its Applications,
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- Francesco Mainardi & Marco Raberto & Rudolf Gorenflo & Enrico Scalas, 2004.
"Fractional calculus and continuous-time finance II: the waiting- time distribution,"
- 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.
- Francesco Mainardi & Marco Raberto & Rudolf Gorenflo & Enrico Scalas, 2000. "Fractional calculus and continuous-time finance II: the waiting-time distribution," Papers cond-mat/0006454, arXiv.org, revised Nov 2000.
- 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.
- 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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