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On the Central Limit Theorems for Forward and Backward Martingales

Authors: Yilun Shang


Let {Xi}i≥1 be a martingale difference sequence with Xi = Si - Si-1. Under some regularity conditions, we show that (X2 1+· · ·+X2N n)-1/2SNn is asymptotically normal, where {Ni}i≥1 is a sequence of positive integer-valued random variables tending to infinity. In a similar manner, a backward (or reverse) martingale central limit theorem with random indices is provided.

Keywords: Central Limit Theorem, martingale difference sequence, backward martingale

Digital Object Identifier (DOI):

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