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