Semi-Markov processes (SMPs) are expressive tools for modelling concurrent systems; they are a generalisation of Markov processes that allow for arbitrarily distributed sojourn times. This paper presents an iterative technique for passage time and transient analysis of large structurally unrestricted semi-Markov processes. Our method is based on the calculation and subsequent numerical inversio...

Semi-Markov processes (SMPs) are expressive tools for modelling parallel and distributed systems; they are a generalisation of Markov processes that allow for arbitrarily distributed sojourn times. This paper presents an iterative technique for transient and passage time analysis of large structurally unrestricted semi-Markov processes. Our method is based on the calculation and subsequent nume...

This article concerns the study of the asymptotic properties of the maximum likelihood estimator (MLE) for the general hidden semi-Markov model (HSMM) with backward recurrence time dependence. By transforming the general HSMM into a general hidden Markov model, we prove that under some regularity conditions, the MLE is strongly consistent and asymptotically normal. We also provide useful expres...

The first application of Semi-Markov Process (SMP) in actuarial field was given by J. Janssen [6]. Many authors successively used these processes and their generalizations In some books it is also shown how it is possible to use these processes in actuarial science, (see Pitacco, Olivieri, [10], CMIR12 [12]).These processes can be generalised introducing a reward structure see for example Howar...