IDENTIFYING A LARGE DEVIATION RATE-FUNCTION

• 成果类型: Article
• 署名作者: DINWOODIE, IH
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176989402
• 发表日期: 1993
• 页码: 216-231
• 关键词: random vectors; bounds

摘要

Assume a sequence of probabilities {P(n)} has a large deviation rate function I. It is proved that I takes a form analogous to a convex conjugate. If I is also assumed convex, then I is a convex conjugate of an explicitly defined function psi. The results are applied to the empirical law of a Markov chain yielding universal bounds on I. Examples are given of Markov chains in which the empirical law has a large deviation rate strictly between the given bounds.