On inequalities for conditional probabilities of unions of events and the conditional Borel–Cantelli lemma

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• 作者：A. N. Frolov
• 关键词：Bonferroni inequalities ; probabilities of unions of events ; conditional Borel–Cantelli lemma ; Borel–Cantelli lemma
• 刊名：Vestnik St. Petersburg University: Mathematics
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：49
• 期：4
• 页码：379-388
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Analysis;
• 出版者：Allerton Press
• ISSN：1934-7855
• 卷排序：49

文摘

New sharp upper and lower bounds for conditional (given a σ-algebra A) probabilities of unions of events and for a generalization of the conditional Borel–Cantelli lemma are obtained. Averaging the left- and right-hand sides of the corresponding inequalities yields bounds better than those obtained by directly estimating the probabilities of events. An example is given. New generalizations of the conditional Borel–Cantelli lemma are also obtained. Averaging yields new versions of this lemma under conditions different from the classical ones.