Davis-type theorems for martingale difference sequences

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

[学科分类] 应用数学