一个具有Markov性的入圈问题  

A Problem on Markov Properties of Circular Interpolation

作　　者：陈玉成[1] 

机构地区：[1]厦门理工学院应用数学学院,福建厦门361024

出　　处：《厦门理工学院学报》2014年第5期98-101,共4页Journal of Xiamen University of Technology

摘　　要：研究序列{Xn},{Xn}满足Xn=Yn(mod 2),其中Yn∈Z+,Y0≥2,Yn+1=Yn+[Yn/2],证明了{Xn}为一独立随机变量序列,并且是一时间齐次Markov链.最后,利用该Markov链{Xn}的性质,证明了入圈问题经过有限次插点,Cm的任意一边上都至少插入一个新点.In this paper, a sequence{Xn} is considered. It satisfies the equationXn = Yn（mod 2） in which Yn∈Z＋, Y0≥2, Yn＋1 = Yn ＋ [Yn/2]. It is proved that the sequence{Xn} is an independent random variables sequence and a time homogeneous Markov chain. Based on the properties of the Markov chain{X n} , it is demonstrated that any edge of the initial circle C m is interpolated at least one new node after finite steps of circular interpolation.

关 键 词：入圈 MARKOV过程 首达概率 

分 类 号：O211.62[理学—概率论与数理统计]