On the large deviation principle for the almost sure CLT

M. A. Lifshits and E. S. Stankevich

Statistics & Probability Letters, 2001, vol. 51, issue 3, 263-267

Abstract: Let Sk be the kth partial sum of real-valued i.i.d. random variables X1, X2,... . Define the random "empirical" measures with logarithmic weightsIf EX1m 0, then Qn satisfies strong large deviations principle, as Heck (Stochastic. Process. Appl. 76 (1998) 61), March and Seppäläinen (J. Theoret. Probab. 10 (1997) 935) have recently proved. We show that the moment assumptions are optimal in this statement.

Keywords: Almost; sure; limit; theorem; Large; deviation; principle (search for similar items in EconPapers)
Date: 2001
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Citations: View citations in EconPapers (2)

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