'Pae multiple time scale decomposition of discrete time, finite state Markov chains is addressed. In [1, 2], the behavior of a continuous time Markov chain is approximated using a fast time scale, e-independent, continuous time process, and a reduced order perturbed process. The procedure can then be iterated to obtain a complete multiple time scale decomposition. In the discrete time case pres...

We consider the problem of performing inference with imprecise continuous-time hidden Markov chains, that is, imprecise continuous-time Markov chains that are augmented with random output variables whose distribution depends on the hidden state of the chain. The prefix ‘imprecise’ refers to the fact that we do not consider a classical continuous-time Markov chain, but replace it with a robust e...

We consider a Hidden Markov Model (HMM) where the integrated continuous-time Markov chain can be observed at discrete time points perturbed by a Brownian motion. The aim is to derive a filter for the underlying continuous-time Markov chain. The recursion formula for the discrete-time filter is easy to derive, however involves densities which are very hard to obtain. In this paper we derive exac...

1 Basic aspects of continuous time Markov chains 3 1.1 Markov property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Regular jump chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Holding times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 Poisson process . . . . . . . . . . . . . . ....