Forgetting the initial distribution for Hidden Markov Models

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...

Full description

Saved in:
Bibliographic Details
Published in:Stochastic processes and their applications 2009-04, Vol.119 (4), p.1235-1256
Main Authors: Douc, R., Fort, G., Moulines, E., Priouret, P.
Format: Article
Language:English
Subjects:
Asymptotic stability
Distribution theory
Exact sciences and technology
Hidden Markov models
Mathematics
Nonlinear filtering
Nonlinear filtering Hidden Markov models Asymptotic stability Total variation norm
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Statistics
Stochastic analysis
Stochastic processes
Total variation norm
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0304-4149
1879-209X
DOI:10.1016/j.spa.2008.05.007