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      Analytic and asymptotic properties of generalized Linnik probability densities

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      Author
      Erdogan, M. B.
      Ostrovskii, I. V.
      Date
      1998-01-15
      Source Title
      Journal of Mathematical Analysis and Applications
      Print ISSN
      0022-247X
      Electronic ISSN
      1096-0813
      Publisher
      Elsevier
      Volume
      217
      Issue
      6
      Pages
      555 - 578
      Language
      English
      Type
      Article
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      Abstract
      This paper studies the properties of the probability density function pα,ν,n(x) of the n-variate generalized Linnik distribution whose characteristic function φα,ν,n(t) is given by where {norm of matrix}t{norm of matrix} is the Euclidean norm of t ∈ ℝn. Integral representations of pα,ν,n(x) are obtained and used to derive the asymptotic expansions of pα,ν,n(x) when {norm of matrix}x{norm of matrix}→0 and {norm of matrix}x{norm of matrix}→∞ respectively. It is shown that under certain conditions which are arithmetic in nature, pα,ν,n(x) can be represented in terms of entire functions. © 2009 Birkhäuser Boston.
      Permalink
      http://hdl.handle.net/11693/11059
      Published Version (Please cite this version)
      http://dx.doi.org/10.1006/jmaa.1997.5734
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