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arXiv · 0707.2796

Random perturbations of stochastic chains with unbounded variable length memory

Pierre Collet·Antonio Galves·Florencia G. Leonardi
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Abstract

We consider binary infinite order stochastic chains perturbed by a random noise. This means that at each time step, the value assumed by the chain can be randomly and independently flipped with a small fixed probability. We show that the transition probabilities of the perturbed chain are uniformly close to the corresponding transition probabilities of the original chain. As a consequence, in the case of stochastic chains with unbounded but otherwise finite variable length memory, we show that it is possible to recover the context tree of the original chain, using a suitable version of the algorithm Context, provided that the noise is small enough.

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Pierre Collet, Antonio Galves, Florencia G. Leonardi. 2007-07-18. Random perturbations of stochastic chains with unbounded variable length memory. https://arxiv.org/abs/0707.2796

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