On selfsimilar Lévy Random Probabilities

Iddo Eliazar

Physica A: Statistical Mechanics and its Applications, 2005, vol. 356, issue 2, 207-240

Abstract: We explore a class of random probabilities induced by the normalization of selfsimilar Lévy Random Measures–random measures whose probability laws are governed by stable one-sided Lévy distributions. Various statistical properties of these random probabilities are analyzed: (i) moment structure; (ii) auto-covariance structure; (iii) one-dimensional and multidimensional tail-probabilities; and (iv) behavior in limiting cases. For the Lévy–Smirnoff case—corresponding to the selfsimilarity index of order 12—an explicit analytic formula for the multidimensional probability density functions is derived. Last, a comparison between the class of selfsimilar Lévy Random Probabilities and the Dirichlet Random Probability (induced by the normalization of the Gamma Random Measure) is conducted, showing the former to be far more robust than the latter.

Keywords: Lévy random measures and probabilities; Selfsimilar Lévy random measures and probabilities; Gamma (search for similar items in EconPapers)
Date: 2005
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437105002347
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:356:y:2005:i:2:p:207-240

DOI: 10.1016/j.physa.2005.02.050

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 ().