Forgetting of the initial distribution for Hidden Markov Models

Details Forgetting of the initial distribution for Hidden Markov Models Forgetting of the initial distribution for Hidden Markov Models

2007-03-28

arxiv.org/abs/math/0703836v1

Stochastic Processes and their Applications (2008) A paraitre

Mathematics

Statistics Theory

Scientific paper

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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