Strong law of large numbers for sums of products
成果类型：
Article
署名作者：
Zhang, CH
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1065725194
发表日期：
1996
页码：
1589-1615
关键词：
摘要：
Let X, X(n), n greater than or equal to 1, be a sequence of independent identically distributed random variables. We give necessary and sufficient conditions for the strong law of large numbers for k = 2 without regularity conditions on X, [GRAPHICS] for k greater than or equal to 3 in three cases: (i) symmetric X, (ii) P{X greater than or equal to 0} = 1 and (iii) regularly varying P{\X\ > x} as x --> infinity, without further conditions, and for general X and k under a condition on the growth of the truncated mean of X. Randomized, centered, squared and decoupled strong laws and general normalizing sequences are also considered.