Hidden Non-markovian Models: Formalization and Solution Approaches

The simulation of real systems involves the building and analysis of models. Various types of discrete stochastic models (DSM) are well suitable to represent real processes with time dependent behavior, however to build a DSM, the system has to be completely observable. Hidden Markov Models (HMM) can model and analyze systems which are only observable through their interaction with the environment, but they are limited due to having a discrete-time Markov chain as hidden process. The combination of DSM and HMM will enable the utilization of the capabilities of HMM to nonMarkovian models. The formalization of these so-called Hidden non-Markovian Models is presented in this paper. Furthermore the existing solution algorithms of HMM are adapted to the new modeling paradigm. However, this adaption was only successful for the evaluation and decoding algorithms and for models of Markov regenerative type, regenerating at every firing of a transition. The new modeling paradigm will be able to solve problems not solvable with existing methods of DSM or HMM alone. With fast and more generally applicable solution algorithms HnMM can be of use in many practical problems existing today.