New Representations for a Semi-Markov Chain and Related Filters
Robert James Elliott, William P. Malcolm · Journal of Stochastic Analysis · 2021
In this article we investigate estimation for a partially observed semi-Markov chain, or a Hidden semi-Markov Model (HsMM).We derive semimartingale dynamics for a semi-Markov chain and give them in a new vector form which explicitly exhibits the times at which jump-events occur and the probabilities of state transitions.However, the most important result is the new vector lattice state-space representation for a general finite-state, discrete-time semi-Markov chain.On this space the semi-Markov chain and its occupation times are a Markov process with dynamics described by finite matrices.These representations are new.Finite dimensional recursive filters are derived for a HsMM.