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Davis-type theorems for martingale difference sequences

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  • George Stoica

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).

Suggested Citation

  • George Stoica, 2005. "Davis-type theorems for martingale difference sequences," International Journal of Stochastic Analysis, Hindawi, vol. 2005, pages 1-7, January.
    • Handle: RePEc:hin:jnijsa:532648
    DOI: 10.1155/JAMSA.2005.159
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