Résumé
The concept of multichain (H)SMM has not been already rigorously formalized, even if a few models have been proposed in literature. This chapter reviews existing multichain HSMMs, and proposes a sound formalization of two classes of models that extend standard and general semi-Markov models to the multichain setting. It then considers the hidden framework and builds various classes of multichain-HSMMs (MHSMMs) that generalize some MHMM structures. A generative definition based on hazard rate instead of probability distribution function enables us to account for flexible interactions between dynamics of observed and hidden chains. Adaptation of these general classes into models for practical situations still raises challenges in terms of inference, but also in terms of parameterization. Indeed, the dimension of the functions (hazard rates and probability distribution functions) involved in the multichain distribution increases with the model richness.