# Stochastic Models for the 3x+1 and 5x+1 Problems

@article{Kontorovich2009StochasticMF, title={Stochastic Models for the 3x+1 and 5x+1 Problems}, author={Alex Kontorovich and J. Lagarias}, journal={arXiv: Number Theory}, year={2009} }

This paper discusses stochastic models for predicting the long-time behavior of the trajectories of orbits of the 3x+1 problem and, for comparison, the 5x+1 problem. The stochastic models are rigorously analyzable, and yield heuristic predictions (conjectures) for the behavior of 3x+1 orbits and 5x+1 orbits.

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#### 13 Citations

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