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Teoriya Veroyatnostei i ee Primeneniya, 2013, Volume 58, Issue 1, Pages 117–132
DOI: https://doi.org/10.4213/tvp4496 (Mi tvp4496) 		 
This article is cited in 25 scientific papers (total in 25 papers)

Generalized hyperbolic laws as limit distributions for random sums

V. Yu. Korolev

M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
Full-text PDF (188 kB) Citations (25)
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DOI: https://doi.org/10.4213/tvp4496
Abstract: A general theorem is proved stating necessary and sufficient conditions for the convergence of the distributions of sums of a random number of independent identically distributed random variables to one-parameter variance-mean mixtures of normal laws. As a corollary, necessary and sufficient conditions for convergence of the distributions of sums of a random number of independent identically distributed random variables to generalized hyperbolic laws are obtained. Convergence rate estimates are presented for a particular case of special continuous time random walks generated by compound doubly stochastic Poisson processes.
Keywords: random sum; generalized hyperbolic distribution; generalized inverse Gaussian distribution; mixture of probability distributions; identifiable mixtures; additively closed family; convergence rate estimate.
Received: 06.04.2012
English version:
Theory of Probability and its Applications, 2014, Volume 58, Issue 1, Pages 63–75
DOI: https://doi.org/10.1137/S0040585X97986400
Bibliographic databases:
Document Type: Article
MSC: 60F05, 60G50
Language: Russian
Citation: V. Yu. Korolev, “Generalized hyperbolic laws as limit distributions for random sums”, Teor. Veroyatnost. i Primenen., 58:1 (2013), 117–132; Theory Probab. Appl., 58:1 (2014), 63–75
Citation in format AMSBIB
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    • This publication is cited in the following 25 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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