A Compact Framework for Hidden Markov Chains with Applications to Fractal Geometry
- 1 September 2008
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 45 (3), 630-639
- https://doi.org/10.1239/jap/1222441819
Abstract
We introduce a class of stochastic processes in discrete time with finite state space by means of a simple matrix product. We show that this class coincides with that of the hidden Markov chains and provides a compact framework for it. We study a measure obtained by a projection on the real line of the uniform measure on the Sierpinski gasket, finding that the dimension of this measure fits with the Shannon entropy of an associated hidden Markov chain.Keywords
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