Strong laws of large numbers for arrays of rowwise independent random elements
Abstract
Let{Xnk}be an array of rowwise independent random elements in a separable Banach space of typep+δwithEXnk=0for allk,n. The complete convergence (and hence almost sure convergence) ofn−1/p∑k=1nXnk to 0,1≤p2, is obtained when{Xnk}are uniformly bounded by a random variableXwithE|X|2p∞. When the array{Xnk}consists of i.i.d, random elements, then it is shown thatn−1/p∑k=1nXnkconverges completely to0if and only ifE‖X11‖2p∞.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jan 01, 1987
- Source ID
- 10.1155/s0161171287000899
Entities
People
- Robert Lee Taylor
- Tien-chung Hu
Organizations
- Air Force Office of Scientific Research
- National Tsing Hua University
- University of Georgia