Limit Theorems for Super-heavy Tailed Random Variables with Truncation: Application to the Super-petersburg Game
by Toshio Nakata  

Vol. 15 No. 2 (2020) P.123~P.141

DOI:	https://doi.org/10.21915/BIMAS.2020202
	10.21915/BIMAS.2020202

ABSTRACT

Motivated by the super-Petersburg game, we consider the super-heavy tailed independent and identically distributed (iid) random variables whose tail are characterized by slow variation. This article explores strong laws of large numbers and central limit theorems for a class of super-heavy tailed random variables with two types of truncations, respectively. We apply our results to the logPareto distributions and the super-Petersburg distributions.

KEYWORDS
super-Petersburg game, super-heavy tail, truncation, strong law of large numbers, central limit theorem, logPareto distribution

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 60G50, 60F15

MILESTONES

Received: 2020-01-26
Revised :
Accepted: 2020-03-11

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