# Loss of memory of hidden Markov models and Lyapunov exponents.

@article{Collet2014LossOM, title={Loss of memory of hidden Markov models and Lyapunov exponents.}, author={P. Collet and Florencia G. Leonardi}, journal={Annals of Applied Probability}, year={2014}, volume={24}, pages={422-446} }

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…

## 10 Citations

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The theory of noise-induced synchronization is introduced together with a more intuitive version of the multiplicative ergodic theory, and then is applied to hidden Markov models for developing an efficient algorithm of parameter inference.

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