Forgetting the initial distribution for Hidden Markov Models

R. Douc, G. Fort, E. Moulines and P. Priouret

Stochastic Processes and their Applications, 2009, vol. 119, issue 4, 1235-1256

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 nonlinear state space model and the stochastic volatility model.

Keywords: Nonlinear; filtering; Hidden; Markov; models; Asymptotic; stability; Total; variation; norm (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (6)

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