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A randomized version of the Collatz \(3x + 1\) problem. (English) Zbl 1329.60252
Summary: We consider a Markov chain on the positive odd integers, which can be viewed as a stochastic version of the Collatz \(3x + 1\) Problem. We show that, no matter its initial value, the chain visits 1 infinitely often. Its values, however, are unbounded.
MSC:
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
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