@article{(Open Science Index):https://publications.waset.org/pdf/15186, title = {On the Central Limit Theorems for Forward and Backward Martingales}, author = {Yilun Shang}, country = {}, institution = {}, abstract = {Let Xii≥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 Nii≥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.}, journal = {International Journal of Mathematical and Computational Sciences}, volume = {5}, number = {4}, year = {2011}, pages = {637 - 640}, ee = {https://publications.waset.org/pdf/15186}, url = {https://publications.waset.org/vol/52}, bibsource = {https://publications.waset.org/}, issn = {eISSN: 1307-6892}, publisher = {World Academy of Science, Engineering and Technology}, index = {Open Science Index 52, 2011}, }