Uniform Estimate for Distributions of the Sum of i.i.d. Random Variables with Fat Tail
Vol. 17 (2010), No. 1, Page 79--121.
Fushiya, Hirotaka; Kusuoka, Shigeo
Uniform Estimate for Distributions of the Sum of i.i.d. Random Variables with Fat Tail
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Abstract:
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.
Keywords: Glu\v skov-Iwasawa local splitting theorem, inverse limit of finite dimensional Lie groups, nilpotent radical of a Lie algebra.
Mathematics Subject Classification (2000): Primary 60F05, Secondary 62E20.
Received: 2009-06-25
