MAJORIZATION, EXPONENTIAL INEQUALITIES AND ALMOST SURE BEHAVIOR OF VECTOR-VALUED RANDOM-VARIABLES

• 成果类型: Article
• 署名作者: BERGER, E
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176990341
• 发表日期: 1991
• 页码: 1206-1226
• 关键词: independent random-variables; iterated logarithm; universal law; sums

摘要

In this paper we describe a general device that allows us to deduce various kinds of theorems (moment estimates, exponential inequalities, strong law of large numbers, stability results, bounded law of the iterated logarithm) for partial sums of independent vector-valued random variables from related results for partial sums of independent real-valued random variables. The concept of majorization will play a key role in our considerations.