Article révisé par les pairs
|This paper gives basic definitions and properties related to what we call the non-homogeneous semi-Markov processes with a finite number of states using the formalism of counting processes, i.e. with intensity functions. We show how it is possible to get generalized Polya processes as a very particular case. We also treat the computational aspect by discretisation and as an application, we develop a social security problem. © 1984.