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In this work, we interest to the estimation of the steady-state probabilities of the two processes (the hidden Markov chain and the emission process) composing a standard Hidden Markov Model. Since the estimation of steady-state Markov chain is well known, more attention will be given to the estimation of the steady-state of the emission process. Among different methods, we will focus more on the technique based on the regenerative notion, often used in steady-state Markov chain simulation. Numerical Monte Carlo simulations are carried to show the usefulness of our proposal and to appreciate the quality of different proposed estimators. [ABSTRACT FROM AUTHOR]

In our paper [A. Nasroallah and K. Elkimakh, HMM with emission process resulting from a special combination of independent Markovian emissions, Monte Carlo Methods Appl. 23 2017, 4, 287–306] we have studied, in a first scenario, the three fundamental hidden Markov problems assuming that, given the hidden process, the observed one selects emissions from a combination of independent Markov chains evolving at the same time. Here, we propose to conduct the same study with a second scenario assuming that given the hidden process, the emission process selects emissions from a combination of independent Markov chain evolving according to their own clock. Three basic numerical examples are studied to show the proper functioning of the iterative algorithm adapted to the proposed model. [ABSTRACT FROM AUTHOR]

One of the most used variants of hidden Markov models (HMMs) is the standard casewhere the time is discrete and the state spaces (hidden and observed spaces) are finite. In this framework, we are interested in HMMs whose emission process results from a combination of independent Markov chains. Principally, we assume that the emission process evolves as follows: given a hidden state realization k at time t, an emission is a realization of a Markov chain Yk't at time t, and for two different hidden states k and k', Yk't and Yk'tt are assumed independent. Given the hidden process, the considered emission process selects its realizations from independent and homogeneous Markov chains evolving simultaneously. In this paper, we propose to study the three known basic problems of such anHMMvariant, by deriving corresponding formulas and algorithms. This allows us to enrich the set of application scenarios of HMMs. Numerical examples are presented to show the applicability of our proposed approach by deriving statistical estimations. [ABSTRACT FROM AUTHOR]