Precise Rates in Log Laws for NA Sequences

Yuexu Zhao

Discrete Dynamics in Nature and Society, 2007, vol. 2007, 1-11

Abstract:

Let X 1 , X 2 , … be a strictly stationary sequence of negatively associated (NA) random variables with E X 1 = 0 , set S n = X 1 + ⋯ + X n , suppose that σ 2 = E X 1 2 + 2 ∑ n = 2 ∞ E X 1 X n > 0 and E X 1 2 < ∞ , if − 1 < α ≤ 1 ; E X 1 2 ( log | X 1 | ) α < ∞ , if α > 1 . We prove lim ε ↓ 0 ε 2 α + 2 ∑ n = 1 ∞ (( log n ) α / n) P ( | S n | ≥ σ ( ε + κ n ) 2 n log n ) = 2 − ( α + 1 ) ( α + 1 ) − 1 E | N | 2 α + 2 , where κ n = O ( 1 / log n ) and N is the standard normal random variable.

Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:089107

DOI: 10.1155/2007/89107

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