# An improved bound for the exponential stability of predictive filters of hidden Markov models

Gerencsér, László and Michaletzky, György and Molnár-Sáska, Gábor
(2007)
*An improved bound for the exponential stability of predictive filters of hidden Markov models.*
Communications in Information and Systems, 7 (2).
pp. 133-152.

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## Abstract

We consider hidden Markov processes in discrete time with a finite state space X and a general observation or read-out space Y, which is assumed to be a Polish space. It is well-known that in the statistical analysis of HMMs the so-called predictive filter plays a fundamental role. A useful result establishing the exponential stability of the predictive filter with respect to perturbations of its initial condition was given in the paper of LeGland and Mevel, MCSS, 2000, in the case, when the assumed transition probability matrix was primitive. The main technical result of the present paper is the extension of the cited result by showing that the random constant and the deterministic positive exponent showing up in the inequality stating exponential stability can be chosen so that for any prescribed s exceeding 1 the s-th exponential moment of the random constant is finite. An application of this result to the estimation of HMMs with primitive transition probability densities will be also briefly presented.

Item Type: | Article |
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Uncontrolled Keywords: | hidden Markov models; predictive filters; exponential stability; risk processes. |

Subjects: | Q Science > QA Mathematics and Computer Science > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány |

Depositing User: | Eszter Nagy |

Date Deposited: | 11 Dec 2012 15:29 |

Last Modified: | 11 Dec 2012 15:29 |

URI: | https://eprints.sztaki.hu/id/eprint/4997 |

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