Abstract
In this article, we study large deviations for sums of independent and identically distributed random variables (random walks) with nonnegative super-heavy tailed distributions. While Hu and Nyrhinen (2004) gave results for heavy tailed distributions, our result is an improvement of one of theirs for super-heavy tailed ones. Moreover, we apply it to the log-Pareto distribution and the distribution for the super-Petersburg game.
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