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Variable Step Random Walks and Self-Similar Distributions.
- Source :
-
Journal of Statistical Physics . Dec2005, Vol. 121 Issue 5/6, p887-899. 13p. 2 Graphs. - Publication Year :
- 2005
-
Abstract
- We study a scenario under which variable step random walks give anomalous statistics. We begin by analyzing the Martingale Central Limit Theorem to find a sufficient condition for the limit distribution to be non-Gaussian. We study the case when the scaling index∼ζ is∼12. For corresponding continuous time processes, it is shown that the probability density function W( x; t) satisfies the Fokker–Planck equation. Possible forms for the diffusion coefficient are given, and related to W( x, t). Finally, we show how a time-series can be used to distinguish between these variable diffusion processes and Lévy dynamics. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00224715
- Volume :
- 121
- Issue :
- 5/6
- Database :
- Academic Search Index
- Journal :
- Journal of Statistical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 19076689
- Full Text :
- https://doi.org/10.1007/s10955-005-5474-y