Sankhya: The Indian Journal of Statistics

2004, Volume 66, Pt. 1, 49--62

On Chover\'s LIL for Weighted Sums of Stable Random Variables

By

Chen Pingyan, Jinan University, Guangzhou, People's Republic of China

SUMMARY. We present an integral test to determine the limiting behaviour of forward delayed sums, Abel and Ces\`aro sums of independent identically distributed  random variables with stable distribution, and deduce Chover type law of the iterated logarithm (LIL) for them.

AMS (1991) subject classification}. 60E07, 60F15, 60G50.

Key words and phrases. Stable random variable, Chover's LIL, integral test,  forward delayed sum, Abel sum, Ces\`aro sum.

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