Marcinkiewicz-Zygmund Weak Laws of Large Numbers for Unconditional Random Elements in Banach Spaces.
SOUTH CAROLINA UNIV COLUMBIA DEPT OF MATHEMATICS AND STATISTICS
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Convergence in probability is obtained for random elements in Banach spaces satisfying various distributional conditions including independence, conditional independence, and unconditional semi-basic, and weights. The constant p, 1 or p or 2, is related to a geometric property of the Banach space and to moment conditions. These results relax the usual hypothesis of identical distributions to tightness and are for conditionally independent and unconditionally semi-basic random elements which are more general than independent random elements with zero means.
- Statistics and Probability