Davis-type theorems for martingale difference sequences

George Stoica

International Journal of Stochastic Analysis, 2005, vol. 2005, 1-7

Abstract:

We study Davis-type theorems on the optimal rate of convergence of moderate deviation probabilities. In the case of martingale difference sequences, under the finite p th moments hypothesis ( 1 ≤ p < ∞ ) , and depending on the normalization factor, our results show that Davis' theorems either hold if and only if p > 2 or fail for all p ≥ 1 . This is in sharp contrast with the classical case of i.i.d. centered sequences, where both Davis' theorems hold under the finite second moment hypothesis (or less).

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:532648

DOI: 10.1155/JAMSA.2005.159

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