Precise asymptotics for a series of T. L. Lai

Author:
Aurel Spataru

Journal:
Proc. Amer. Math. Soc. **132** (2004), 3387-3395

MSC (2000):
Primary 60G50, 60E15

DOI:
https://doi.org/10.1090/S0002-9939-04-07524-0

Published electronically:
June 21, 2004

MathSciNet review:
2073316

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be i.i.d. random variables with , and set . We prove that, for

under the assumption that and 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:
https://doi.org/10.1090/S0002-9939-04-07524-0

Keywords:
Tail probabilities of sums of i.i.d. random variables,
moderate deviations,
Lai law

Received by editor(s):
August 1, 2003

Published electronically:
June 21, 2004

Communicated by:
Richard C. Bradley

Article copyright:
© Copyright 2004
American Mathematical Society