On the Central Limit Theorems for Forward and Backward Martingales
نویسنده
چکیده
Let {Xi}i≥1 be a martingale difference sequence with Xi = Si − Si−1. Under some regularity conditions, we show that (X 1+· · ·+X2 Nn)SNn 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.
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