Strong Laws of Large Numbers for Arrays of Rowwise Independent Random Elements.
Abstract
Let (X sub nk) be an array of rowwise independent random elements in a separable Banach space of type p + delta with EX sub nk = 0 for all k, n. The complete convergence (and hence almost sure convergence) of n to the -1/p power sum from k = 1 ton of X sub nk to 0, 1 < or = p < 2, is obtained when (X sub nk) are uniformly bounded by a random variable X with abs. val X to the 2p power < infinity. When the array (X sub nk) consists of i.i.d. random elements, then it is shown that n to the -1/p power from k = 1 ton of X sub nk converges completely to 0 if and only if E abs. val. of X sub 11 to the 2p power < infinity.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1986
- Accession Number
- ADA177179
Entities
People
- Robert L. Taylor
- Tien-chung Hu
Organizations
- University of North Carolina at Chapel Hill