Precise asymptotics for a series of T. L. Lai
Author:
Aurel Spataru
Journal:
Proc. Amer. Math. Soc. 132 (2004), 33873395
MSC (2000):
Primary 60G50, 60E15
Published electronically:
June 21, 2004
MathSciNet review:
2073316
Fulltext PDF Free Access
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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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 ROZOVSKY, L. V. (2003). On precise asymptotics in the weak law of large numbers for sums of independent random variables with a common distribution function from the domain of attraction of a stable law (Russian). Teoriya Veroyatn. Primen. 48, no. 3.
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 SCHEFFLER, H.P. (2003). Precise asymptotics in Spitzer's and BaumKatz law of large numbers: the semistable case. J. Math. Anal. Appl. 288, 285298.
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 SPATARU, A. (1999). Precise asymptotics in Spitzer's law of large numbers. J. Theor. Probab. 12, 811819. MR 2000j:60035
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 SPATARU, A. (2002). Exact asymptotics in loglog laws for random fields. J. Theor. Probab., to appear.
 14.
 WANG Y. and YANG, Y. (2003). A general law of precise asymptotics for the counting process of record times. J. Math. Anal. Appl. 286, 753764.
 15.
 WANG Y., YAN J., and YANG Y. (2003). The precise asymptotics for the order statistics generated by the random samples of maximum domain of attraction of the Fréchet distribution. Preprint, Dept. of Mathematics, Soochow Univ.
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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:
http://dx.doi.org/10.1090/S0002993904075240
PII:
S 00029939(04)075240
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
