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题名: Selecting The Last Consecutive Record in a Record Process
作者: Hsiau, Shoou-Ren
贡献者: 數學系
关键词: Optimal stopping;Threshold type;Consecutive record;Monotone stopping rule;Record process
日期: 2010-09
上传时间: 2013-06-05T07:41:25Z
出版者: Applied Probability Trust
摘要: Suppose that I1, I2, ⋯ is a sequence of independent Bernoulli random variables with E(In) = λ/(λ + n - 1), n = 1, 2, ⋯. If λ is a positive integer k, {In}n≥1 can be interpreted as a k-record process of a sequence of independent and identically distributed random variables with a common continuous distribution. When In-1I n = 1, we say that a consecutive k-record occurs at time n. It is known that the total number of consecutive k-records is Poisson distributed with mean k. In fact, for general λ > 0, ∑∞n=2 In-1In is Poisson distributed with mean λ. In this paper, we want to find an optimal stopping time τλ which maximizes the probability of stopping at the last n such that I n-1In = 1. We prove that τλ is of threshold type, i.e. there exists a τλ ε ℕ such that τλ = min{n | n ≥ τλ, In-1In = 1}. We show that τλ is increasing in λ and derive an explicit expression for τλ. We also compute the maximum probability Qλ of stopping at the last consecutive record and study the asymptotic behavior of Qλ as λ→∞.
關聯: Advances in Applied Probability, 42(3): 739-760
显示于类别:[數學系] 期刊論文


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