A randomized version of the Collatz problem

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• 作者：Aristides V. Doumas ; ^{aris.doumas@hotmail.com" class="auth_mail" title="E-mail the corresponding author} ; Vassilis G. Papanicolaou ^{papanico@math.ntua.gr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：60J10
• 刊名：Statistics & Probability Letters
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：109
• 期：Complete
• 页码：39-44
• 全文大小：371 K

文摘

We consider a Markov chain on the positive odd integers, which can be viewed as a stochastic version of the Collatz 3x+1$3x+1$ Problem. We show that, no matter its initial value, the chain visits 1 infinitely often. Its values, however, are unbounded.