A characterization of progressively equivalent probability measures preserving the structure of a compound mixed renewal process

Abstract

Generalizing earlier work of Delbaen & Haezendonck for given compound mixed renewal process S under a probability measure P , we characterize all those probability measures Q on the domain of P such that Q and P are progressively equivalent and S remains a compound mixed renewal process under Q with improved properties. As a consequence, we prove that any compound mixed renewal process can be converted into a compound mixed Poisson one through a change of measures.