Abstract:
Multidimensional generalizations of the Tauberian theorems of Karamata are obtained, along with two applications of them to the investigation of Bellman–Harris branching processes.
Bibliography: 10 titles.
Citation:
A. L. Yakymiv, “Multidimensional Tauberian theorems and their application to Bellman–Harris branching processes”, Math. USSR-Sb., 43:3 (1982), 413–425
\Bibitem{Yak81}
\by A.~L.~Yakymiv
\paper Multidimensional Tauberian theorems and their application to Bellman--Harris branching processes
\jour Math. USSR-Sb.
\yr 1982
\vol 43
\issue 3
\pages 413--425
\mathnet{http://mi.mathnet.ru/eng/sm2407}
\crossref{https://doi.org/10.1070/SM1982v043n03ABEH002572}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=628221}
\zmath{https://zbmath.org/?q=an:0494.60087|0469.60085}
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https://doi.org/10.1070/SM1982v043n03ABEH002572
https://www.mathnet.ru/eng/sm/v157/i3/p463
This publication is cited in the following 15 articles:
A. L. Yakymiv, “Some properties of regularly varying functions and series in the orthant”, Springer Proc. Math. Statist., 358 (2021), 373–385
A. L. Yakymiv, “Multivariate regular variation in probability theory”, J. Math. Sci. (N.Y.), 246:4 (2020), 580–586
A. L. Yakymiv, “Abelian theorem for the regularly varying measure and its density in orthant”, Theory Probab. Appl., 64:3 (2019), 385–400
Yu. N. Drozhzhinov, “Multidimensional Tauberian theorems for generalized functions”, Russian Math. Surveys, 71:6 (2016), 1081–1134
A. L. Yakymiv, “Tauberian theorem for generating functions of multiple series”, Theory Probab. Appl., 60:2 (2016), 343–347
V. A. Vatutin, V. A. Topchiǐ, “Catalytic branching random walks in Zd with branching at the origin”, Siberian Adv. Math., 23:2 (2013), 125–153
Omey E., Vesilo R., “The Difference Between the Product and the Convolution Product of Distribution Functions in R-N”, Publ. Inst. Math.-Beograd, 89:103 (2011), 19–36
A. P. Shashkin, “On the central limit Newman theorem”, Theory Probab. Appl., 50:2 (2006), 330–337
A. L. Yakymiv, “Tauberian theorems and asymptotics of infinitely divisible
distributions in a cone”, Theory Probab. Appl., 48:3 (2004), 493–505
A. P. Shashkin, “Invariance principle for a (BL,θ)-dependent random field”, Russian Math. Surveys, 58:3 (2003), 617–618
Yu. N. Drozhzhinov, B. I. Zavialov, “Theorems of Hardy–Littlewood type for signed measures on a cone”, Sb. Math., 186:5 (1995), 675–693
I. S. Molchanov, “Limit Theorems for Unions of Random Sets under Multiplicative Normalization”, Theory Probab Appl, 38:3 (1993), 541
Boimatov K., “Multidimensional Spectral Asymptotics for Elliptic-Operators on Domains Satisfying the Cone Condition”, 316, no. 1, 1991, 14–18
A. L. Yakymiv, “On the number of A-permutations”, Math. USSR-Sb., 66:1 (1990), 301–311
Iakymiv A., “Multidimensional Tauberian-Theorems of the Karamata, Keldysh, and Littlewood Type”, 270, no. 3, 1983, 558–561
Citation in format AMSBIB
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