Random perturbations of stochastic processes with unbounded variable length memory

Author(s)

Collet, Pierre ^[1] ; Galves, Antonio ^[2] ; Leonardi, Florencia ^[2]

Affiliation

^[1] Ecole Polytech, Ctr Phys Theor, CNRS, UMR 7644, F-91128 Palaiseau - France

^[2] Univ Sao Paulo, Inst Matemat & Estat, BR-05315970 Sao Paulo - Brazil

• Document type: Journal article
• Source: ELECTRONIC JOURNAL OF PROBABILITY; v. 13, p. 1345-1361, AUG 25 2008.
• Web of Science Citations: 6

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. (AU)

• FAPESP's process: 03/09930-9 - Stochastic behavior, critical phenomena and rhythmic patterns identification in natural languages
• Grantee: Jefferson Antonio Galves
• Support Opportunities: PRONEX Research - Thematic Grants