Μεμειγμένες ανανεωτικές στοχαστικές διαδικασίες με εφαρμογές στα αναλογιστικά υποδείγματα
Τζανίνης, Σπυρίδων Μ.
The mixed renewal processes are investigated and some applications of the above in actuarial models are given. Since, mixed Poisson processes are the simplest case of the mixed renewal ones we first conduct a comparative study of the various definitions of mixed Poisson processes. Next, Huang's definition for mixed renewal processes is studied, several properties of them are investigated and Hung's result that a mixed renewal process is a Markovian one if and only it is a mixed Poisson one. Furthermore, a second definition for mixed renewal processes is given and some characterizations of mixed renewal processes in terms of disintegrations and of exchangeability are provi¬ded. As consequence of these characterizations, it is shown that the two definitions are coinciding in the most cases of applications in Probability Theory. As a second conse¬quence, an existence result of  for mixed renewal processes, providing at the same time a constructive method for them is presented. As an application some concrete examples of mixed renewal processes are given and the corresponding disintegrated measures are explicitly computed. Finally, some applications to actuarial models are given.