期刊
JOURNAL OF MATHEMATICAL PHYSICS
卷 53, 期 5, 页码 -出版社
AMER INST PHYSICS
DOI: 10.1063/1.4709443
关键词
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资金
- Agence Nationale de la Recherche (Paris, France) [ANR-08-BLAN-0243-2]
- PAN/French National Center for Scientific Research (CNRS) [4339]
- Fundacao de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP, Brasil) [2010/15698-5]
We present a method of generation of exact and explicit forms of one-sided, heavy-tailed Levy stable probability distributions g(alpha)(x), 0 <= x < infinity, 0 < alpha < 1. We demonstrate that the knowledge of one such a distribution g a ( x) suffices to obtain exactly g(alpha)p ( x), p = 2, 3, .... Similarly, from known g(alpha)(x) and g(beta)(x), 0 < alpha, beta < 1, we obtain g(alpha beta)( x). The method is based on the construction of the integral operator, called Levy transform, which implements the above operations. For a rational, alpha = l/k with l < k, we reproduce in this manner many of the recently obtained exact results for g(l/k)(x). This approach can be also recast as an application of the Efros theorem for generalized Laplace convolutions. It relies solely on efficient definite integration. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4709443]
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