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Teoriya Veroyatnostei i ee Primeneniya, 1998, Volume 43, Issue 4, Pages 786–792
DOI: https://doi.org/10.4213/tvp2080 (Mi tvp2080) 		 
This article is cited in 20 scientific papers (total in 20 papers)

Short Communications

On convergence of distributions of compound Cox processes to stable laws

V. Yu. Korolev

M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
Full-text PDF (1116 kB) Citations (20)
DOI: https://doi.org/10.4213/tvp2080
Abstract: Necessary and sufficient conditions are presented for weak convergence of one-dimensional distributions of compound doubly stochastic Poisson processes in which jumps have finite variances, whereas no moment-type restrictions are imposed on the controlling process. Criteria of convergence of distributions of these processes to stable laws are presented.
Keywords: doubly stochastic Poisson process (Cox process), compound Cox process, heavy tails, strictly stable distribution.
Received: 13.11.1997
English version:
Theory of Probability and its Applications, 1999, Volume 43, Issue 4, Pages 644–650
DOI: https://doi.org/10.1137/S0040585X97977227
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. Yu. Korolev, “On convergence of distributions of compound Cox processes to stable laws”, Teor. Veroyatnost. i Primenen., 43:4 (1998), 786–792; Theory Probab. Appl., 43:4 (1999), 644–650
Citation in format AMSBIB
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\paper On convergence of~distributions of~compound Cox processes to~stable laws
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\transl
\jour Theory Probab. Appl.
\yr 1999
\vol 43
\issue 4
\pages 644--650
\crossref{https://doi.org/10.1137/S0040585X97977227}
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  • https://www.mathnet.ru/eng/tvp/v43/i4/p786
    • This publication is cited in the following 20 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теория вероятностей и ее применения Theory of Probability and its Applications
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