Regularly Varying of the Normalizing Constants in the Theorem of Convergence to a Positive Stable Distribution
DOI:
https://doi.org/10.51408/1963-0131Keywords:
Insurance, random variable, regularly varying function, slowly varying function, stable distributionAbstract
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
V. Feller, An Introduction to Probability Theory and its Applications, vol. 2, MIR printing house, Moscow, 1984.
E. Seneta, Regularly Varying Functions, Nauka Printing House, Moscow, 1985.
R. L. Dobrushin, “Lemma on the limit of a complex random function", UMN, pp. 157-159, 1955.
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.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Robert N. Chitchyan
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
