期刊名称：Sankhya. Series A, mathematical statistics and probability
印刷版ISSN：0976-836X
电子版ISSN：0976-8378
出版年度：2010
卷号：72
期号：2
页码：344-358
DOI：10.1007/s13171-010-0020-7
语种：English
出版社：Indian Statistical Institute
摘要：In this paper, we introduce the concept of multiparameter martingale differences and provide a characterization of p -uniformly smooth Banach spaces in terms of an inequality for multiparameter martingale differences. Then we apply this result to establish some weak laws of large numbers, where the classical degenerate convergence criterion and Kolmogorov-Feller weak law of large numbers will be extended to d -dimensional adapted arrays in Banach spaces. Some special cases of our results are presented as corollaries, and illustrative examples are provided.
关键词：p -uniformly smooth Banach space ; adapted array ; martingale difference array ; weak law of large numbers
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