%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