Abstract
We study Davis-type theorems on the moderate deviation probabilities of martingale differences with finite pth moments ( 1 ⩽ p < ∞ ) . We prove that Davis' first result holds if p > 4 and fails if 1 ⩽ p < 4 , and Davis' second result holds if p > 2 and fails if 1 ⩽ p < 2 .
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