%0 Journal Article %A Yilun Shang %D 2011 %J International Journal of Mathematical and Computational Sciences %B World Academy of Science, Engineering and Technology %I Open Science Index 52, 2011 %T On the Central Limit Theorems for Forward and Backward Martingales %U https://publications.waset.org/pdf/15186 %V 52 %X 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. %P 637 - 640