Regularly Varying of the Normalizing Constants in the Theorem of Convergence to a Positive Stable Distribution

Authors

  • Robert N. Chitchyan Institute for Informatics and Automation Problems of NAS RA

Keywords:

Insurance, random variable, regularly varying function, slowly varying function, stable distribution

Abstract

This article examines the behavior of the normalizing constants in V. Feller’s theorem on the convergence of distributions for sums of independent, identically distributed random variables with heavy tails at infinity. It is proved that, in this setting, the normalizing constant is regularly varying at infinity.

References

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J. Magyorodi, Limit distribution of sequences of random variables with random indices, Transactions of the Fourth Prague Conference on Information Theory, Statistical Decision Functions, Random Processes, Prague, pp. 463–470, 1967.

L. A. Zolotukhin, On the asymptotic distribution of sequences with random indices, Mathematical Notes of the Academy of Sciences of the USSR, vol. 6, pp. 887–891, 1969.

R. N. Chitchyan, On the asymptotic behaviour of distributions of random sequences with random indices and regularly varying "tails", Abstracts of the Second International Conference "Mathematics in Armenia: Advances and Perspectives", Tsaghkadzor, Armenia, pp. 82–83, 2013.

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Published

2025-06-01

How to Cite

Chitchyan, R. N. (2025). Regularly Varying of the Normalizing Constants in the Theorem of Convergence to a Positive Stable Distribution. Mathematical Problems of Computer Science, 63, 54–59. Retrieved from https://mpcs.sci.am/index.php/mpcs/article/view/884