Loss of Memory of Hidden Markov Models and Lyapunov Exponents

by Collet, P. and Leonardi, F.

In this paper we prove that the asymptotic rate of exponential loss of memory of a finite state hidden Markov model is bounded above by the difference of the first two Lyapunov exponents of a certain product of matrices. We also show that this bound is in fact realized, namely for almost all realizations of the observed process we can find symbols where the asymptotic exponential rate of loss of memory attains the difference of the first two Lyapunov exponents. These results are derived in particular for the observed process and for the filter; that is, for the distribution of the hidden state conditioned on the observed sequence. We also prove similar results in total variation.

The whole paper is available here: www.ime.usp.br/~leonardi/artigos/collet_and_leonardi_2014.pdf

NeuroCineMat
Featuring this week:
Newsletter

Stay informed on our latest news!



Previous issues

Podcast A Matemática do Cérebro
Podcast A Matemática do Cérebro
NeuroMat Brachial Plexus Injury Initiative
Logo of the NeuroMat Brachial Plexus Injury Initiative
Neuroscience Experiments System
Logo of the Neuroscience Experiments System
NeuroMat Parkinson Network
Logo of the NeuroMat Parkinson Network
NeuroMat's scientific-dissemination blog
Logo of the NeuroMat's scientific-dissemination blog