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Precise asymptotics for a series of T. L. Lai
Author(s):
Aurel
Spataru
Journal:
Proc. Amer. Math. Soc.
132
(2004),
3387-3395.
MSC (2000):
Primary 60G50, 60E15
Posted:
June 21, 2004
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Abstract:
Let  be i.i.d. random variables with  , and set  . We prove that, for 
under the assumption that  and ![$E[\left\vert X\right\vert ^{2p}(\log ^{+}\left\vert X\right\vert )^{-p}]<\infty .$](/proc/2004-132-11/S0002-9939-04-07524-0/gif-abstract0/img7.gif) Necessary and sufficient conditions for the convergence of the sum above were established by Lai (1974).
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Additional Information:
Aurel
Spataru
Affiliation:
Institute of Mathematical Statistics and Applied Mathematics, Romanian Academy, Calea 13 Septembrie.13, 76100 Bucharest, Romania
Email:
aspataru@pcnet.ro
DOI:
10.1090/S0002-9939-04-07524-0
PII:
S 0002-9939(04)07524-0
Keywords:
Tail probabilities of sums of i.i.d. random variables,
moderate deviations,
Lai law
Received by editor(s):
August 1, 2003
Posted:
June 21, 2004
Communicated by:
Richard C. Bradley
Copyright of article:
Copyright
2004,
American Mathematical Society
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