Non-extensive random walks

C. Anteneodo

Physica A: Statistical Mechanics and its Applications, 2005, vol. 358, issue 2, 289-298

Abstract: Stochastic variables whose addition leads to q-Gaussian distributions Gq(x)∝[1+(q-1)βx2]+1/(1-q) (with β>0, 1⩽q<3 and where [f(x)]+=max{f(x),0}) as limit law for a large number of terms are investigated. Random walk sequences related to this problem possess a simple additive–multiplicative structure commonly found in several contexts, thus justifying the ubiquity of those distributions. A characterization of the statistical properties of the random walk step lengths is performed. Moreover, a connection with non-linear stochastic processes is exhibited. q-Gaussian distributions have special relevance within the framework of non-extensive statistical mechanics, a generalization of the standard Boltzmann–Gibbs formalism, introduced by Tsallis over one decade ago. Therefore, the present findings may give insights on the domain of applicability of such generalization.

Keywords: Non-extensivity; Random-walks; Anomalous diffusion (search for similar items in EconPapers)
Date: 2005
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437105006436
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:358:y:2005:i:2:p:289-298

DOI: 10.1016/j.physa.2005.06.052

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().