Loading...

Please use this identifier to cite or link to this item:
http://ir.ncue.edu.tw/ir/handle/987654321/16713

Title:  Selecting The Last Consecutive Record in a Record Process 
Authors:  Hsiau, ShoouRen 
Contributors:  數學系 
Keywords:  Optimal stopping;Threshold type;Consecutive record;Monotone stopping rule;Record process 
Date:  201009

Issue Date:  20130605T07:41:25Z

Publisher:  Applied Probability Trust 
Abstract:  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 krecord process of a sequence of independent and identically distributed random variables with a common continuous distribution. When In1I n = 1, we say that a consecutive krecord occurs at time n. It is known that the total number of consecutive krecords is Poisson distributed with mean k. In fact, for general λ > 0, ∑∞n=2 In1In 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 n1In = 1. We prove that τλ is of threshold type, i.e. there exists a τλ ε ℕ such that τλ = min{n  n ≥ τλ, In1In = 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→∞. 
Relation:  Advances in Applied Probability, 42(3): 739760 
Appears in Collections:  [math] Periodical Articles

Files in This Item:
File 
Size  Format  
2020101410002.pdf  91Kb  Adobe PDF  276  View/Open 

All items in NCUEIR are protected by copyright, with all rights reserved.
