Geodesic
Limit distributions for doubly stochastically rarefied renewal processes and their properties
Teoriâ veroâtnostej i ee primeneniâ, Tome 61 (2016) no. 4, pp. 753-773

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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, Weibull distribution, Linnik distribution
Mots-clés : stable distribution, Mittag-Leffler distribution, Laplace distribution. 
@article{TVP_2016_61_4_a6,
     author = {V. Yu. Korolev},
     title = {Limit distributions for doubly stochastically rarefied renewal processes and their properties},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {753--773},
     publisher = {mathdoc},
     volume = {61},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2016_61_4_a6/}
}
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V. Yu. Korolev. Limit distributions for doubly stochastically rarefied renewal processes and their properties. Teoriâ veroâtnostej i ee primeneniâ, Tome 61 (2016) no. 4, pp. 753-773. http://geodesic.mathdoc.fr/item/TVP_2016_61_4_a6/