Almost sure convergence and complete convergence for the weighted sums of martingale differences
β Scribed by Deng Ai-jiao; Liu Jing-jun
- Publisher
- Wuhan University
- Year
- 1999
- Tongue
- English
- Weight
- 328 KB
- Volume
- 4
- Category
- Article
- ISSN
- 1007-1202
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Under general weighting coe cient, we obtain the complete convergence for weighted sums of negatively associated (NA) sequences, and discuss its necessity. The results on i.i.d. setting of Chow [
For each n, let ( S n k ) , 1 S k s k,, be a mean zero square -integrable martingale adapted to increasing a-fields ($nk), O s k s h n , and let ( b n k ) , OSkaE,, be a system of random variables such that bno=O -=bnl-=... -= bnkn= 1 and such that bnk is Snn,k-l measurable for each k. We present su
We discuss complete convergence for weighted sums of negatively associated (NA) random variables. The result on i.i.d. case of Li et al. (J. Theoret. Probab. 8 (1995) 49 -76) is generalized and extended. Also, Gut's (Probab. Theory Related Fields 97 (1993) 169 -178) result on CesΓ aro summation of i