Graduate School of Mathematical Sciences, The University of Tokyo
Journal of Mathematical Sciences, The University of Tokyo. Vol. 17 (2010), No. 1, Page 79-121
The research on asymptotic behavior of distributions of the sum of i.i.d random variables has a long history and a lot of facts are known. The authors consider the case where the distribution of a random variable has the second moment but has a fat tail, and they show a new limit theorem for large deviations.