Weak convergence of random sums under nonrandom centering
โ Scribed by V. M. Kruglov
- Publisher
- Springer US
- Year
- 1995
- Tongue
- English
- Weight
- 399 KB
- Volume
- 76
- Category
- Article
- ISSN
- 1573-8795
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
We find a simple necessary and sufficient condition for the convergence of nonrandomly centered random sums under the hypothesis that sure sums of the same random variables converge. The result contained here subsumes previous results of the authors and others and gives a unified treatment of some a
Let mlzk be a median of X,, and put S, = X,, + + X , + . . . +Xnkrt-A,, where {A,, n= 1, 2, . . .} is a sequence of constants. S, and X,, are subject to F, and F,,, respectively. The problem is the existence of a non-defective limit distribution for {Fn, n = 1, 2, . . .} in the sence of weak conver