# Mathematics Colloquia and Seminars

### Bounds on convergence of the entropy rate block estimates for exact hidden Markov models.

Mathematical Physics & Probability

 Speaker: Nick Travers, UC Davis Location: 2112 MSB Start time: Wed, Apr 3 2013, 4:10PM

A hidden Markov model (HMM) is said to be exactly synchronizing or simply exact if there is some finite word $w$ such that an observer knows the internal state of the model with certainty after observing the output $w$. We provide an exponential upper bound for convergence of the entropy rate block estimates $h(n) = H(X_n|X_1,...,X_{n-1})$ in exact HMMs with finite state sets and output alphabets. We believe the bound should often be tight.