ON A DOMINATION OF SUMS OF RANDOM-VARIABLES BY SUMS OF CONDITIONALLY INDEPENDENT ONES

• 成果类型: Article
• 署名作者: HITCZENKO, P
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176988868
• 发表日期: 1994
• 页码: 453-468
• 关键词: INEQUALITIES; martingales; SEQUENCES; bounds

摘要

It is known that if (X(n)) and (Y(n)) are two (F(n))-adapted sequences of random variables such that for each k greater-than-or-equal-to 1 the conditional distributions of X(k) and Y(k), given F(k-1), coincide a.s., then the following is true: \\SIGMAX(k)\\p less-than-or-equal-to B(p)\\SIGMA Y(k)\\p, 1 less-than-or-equal-to p < infinity, for some constant B(p) depending only on p. The aim of this paper is to show that if a sequence (Y(n)) is conditionally independent, then the constant B(p) may actually be chosen to be independent of p. This significantly improves all hitherto known estimates on B(p) and extends an earlier result of Mass on randomly stopped sums of independent random variables as well as our recent result dealing with martingale transforms of Rademacher sequences.