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.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 349 (2005)
Issue (Month): 3 ()
|Contact details of provider:|| Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- Enrico Scalas & Rudolf Gorenflo & Francesco Mainardi, 2004.
"Fractional calculus and continuous-time finance,"
- Scalas, Enrico & Gorenflo, Rudolf & Mainardi, Francesco, 2000. "Fractional calculus and continuous-time finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 376-384.
- 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, 2004. "Fractional calculus and continuous-time finance II: the waiting- time distribution," Finance 0411008, EconWPA.
- 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.
- 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.
When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:349:y:2005:i:3:p:375-420. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If references are entirely missing, you can add them using this form.