Yilun Shang
On the Central Limit Theorems for Forward and Backward Martingales
637 - 640
2011
5
4
International Journal of Mathematical and Computational Sciences
https://publications.waset.org/pdf/15186
https://publications.waset.org/vol/52
World Academy of Science, Engineering and Technology
Let Xii≥1 be a martingale difference sequence with
Xi Si Si1. Under some regularity conditions, we show that
(X2
1· · ·X2N
n)12SNn is asymptotically normal, where Nii≥1
is a sequence of positive integervalued random variables tending
to infinity. In a similar manner, a backward (or reverse) martingale
central limit theorem with random indices is provided.
Open Science Index 52, 2011