Hitting probabilities and large deviations

• 成果类型: Article
• 署名作者: Collamore, JF
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 1996
• 页码: 2065-2078
• 关键词: markov additive processes; LIMIT-THEOREMS

摘要

Let {Y-n}(n is an element of Z+) be a sequence of random variables in R(d) and let A subset of R(d). Then P{Y-n is an element of A for some n} is the hitting probability of the set A by the sequence {Y-n}. We consider the asymptotic behavior, as m --> infinity, of P{Y-n is an element of mA, some n} = P{hitting mA} whenever (1) the probability law of Y-n/n satisfies the large deviation principle and (2) the central tendency of Y-n/n is directed away from the given set A. For a particular function (I) over tilde, we show P{Y-n is an element of mA, some n} approximate to exp(<-m(I)over tilde>(A)).