Mathematics – Probability
Scientific paper
2008-04-17
Annals of Applied Probability 2009, Vol. 19, No. 3, 1172-1199
Mathematics
Probability
Published in at http://dx.doi.org/10.1214/08-AAP576 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst
Scientific paper
10.1214/08-AAP576
A hidden Markov model is called observable if distinct initial laws give rise to distinct laws of the observation process. Observability implies stability of the nonlinear filter when the signal process is tight, but this need not be the case when the signal process is unstable. This paper introduces a stronger notion of uniform observability which guarantees stability of the nonlinear filter in the absence of stability assumptions on the signal. By developing certain uniform approximation properties of convolution operators, we subsequently demonstrate that the uniform observability condition is satisfied for various classes of filtering models with white-noise type observations. This includes the case of observable linear Gaussian filtering models, so that standard results on stability of the Kalman--Bucy filter are obtained as a special case.
No associations
LandOfFree
Uniform observability of hidden Markov models and filter stability for unstable signals does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Uniform observability of hidden Markov models and filter stability for unstable signals, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Uniform observability of hidden Markov models and filter stability for unstable signals will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-507203