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Forgetting of the initial distribution for Hidden Markov Models

Randal Douc·Gersende Fort·Eric Moulines·Pierre Priouret
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Abstract

The forgetting of the initial distribution for discrete Hidden Markov Models (HMM) is addressed: a new set of conditions is proposed, to establish the forgetting property of the filter, at a polynomial and geometric rate. Both a pathwise-type convergence of the total variation distance of the filter started from two different initial distributions, and a convergence in expectation are considered. The results are illustrated using different HMM of interest: the dynamic tobit model, the non-linear state space model and the stochastic volatility model.

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Randal Douc, Gersende Fort, Eric Moulines, Pierre Priouret. 2007-03-28. Forgetting of the initial distribution for Hidden Markov Models. https://arxiv.org/abs/math/0703836

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