DISTINGUISHING A SEQUENCE OF RANDOM-VARIABLES FROM A RANDOM TRANSLATE OF ITSELF

• 成果类型: Article
• 署名作者: OKAZAKI, Y; SATO, H
• 署名单位: Kyushu University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176988742
• 发表日期: 1994
• 页码: 1092-1096
• 关键词: absolute continuity; product measure

摘要

Let X = {X(k)} be an i.i.d. real random sequence, let epsilon = {epsilon(k)} be a Rademacher sequence independent of X and let a = {a(k)} be a deterministic real sequence. The aim of this paper is to prove that the mutual absolute continuity of probability measures induced by {X(k)} and {X(k) + a(k)epsilon(k)} implies a is-an-element-of l4. This is a generalization of a result of Shepp.