Open Access
2008 Random perturbations of stochastic processes with unbounded variable length memory
Pierre Collet, Antonio Galves, Florencia Leonardi
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Electron. J. Probab. 13: 1345-1361 (2008). DOI: 10.1214/EJP.v13-538


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 Leonardi. "Random perturbations of stochastic processes with unbounded variable length memory." Electron. J. Probab. 13 1345 - 1361, 2008.


Accepted: 25 August 2008; Published: 2008
First available in Project Euclid: 1 June 2016

zbMATH: 1206.62160
MathSciNet: MR2438809
Digital Object Identifier: 10.1214/EJP.v13-538

Primary: 62M09
Secondary: 60G99

Keywords: algorithm Context , Chains of infinite order , chains with unbounded variable length memory , context trees , Random perturbations , variable length Markov chains

Vol.13 • 2008
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