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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