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Teoriya Veroyatnostei i ee Primeneniya, 2016, Volume 61, Issue 4, Pages 753–773
DOI: https://doi.org/10.4213/tvp5086 (Mi tvp5086) 		 
This article is cited in 10 scientific papers (total in 10 papers)

Limit distributions for doubly stochastically rarefied renewal processes and their properties

V. Yu. Korolevabc

a Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
b Hangzhou Dianzi University, Zhejiang
c Federal Research Center "Computer Science and Control" of Russian Academy of Sciences
Full-text PDF (285 kB) Citations (10)
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DOI: https://doi.org/10.4213/tvp5086
Abstract: A limit theorem is proved for doubly stochastically rarefied renewal processes. It is shown that under rather general conditions, as limit laws in limit theorems for mixed geometric random sums, there appear mixed exponential and mixed Laplace distributions. Some known and new properties of these distributions are reviewed. Also, some nonobvious properties of special representatives of these classes (the Weibull, Mittag-Leffler, Linnik, and other distributions) are described.
Keywords: doubly stochastically rarefied renewal process, mixed geometric distribution, mixed geometric random sum, mixed exponential distribution, stable distribution, Weibull distribution, Mittag-Leffler distribution, Linnik distribution, Laplace distribution.
Funding agency Grant number
Russian Science Foundation 14-11-00364
Received: 05.10.2016
English version:
Theory of Probability and its Applications, 2017, Volume 61, Issue 4, Pages 649–664
DOI: https://doi.org/10.1137/S0040585X97T98840X
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. Yu. Korolev, “Limit distributions for doubly stochastically rarefied renewal processes and their properties”, Teor. Veroyatnost. i Primenen., 61:4 (2016), 753–773; Theory Probab. Appl., 61:4 (2017), 649–664
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tvp/v61/i4/p753
    • This publication is cited in the following 10 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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