Mixed exponential processes (Q2726261)

Mixtures of probability distributions permit to define new statistical models. These families often enjoy some important geometrical properties such as convexity and completeness. As the classical example of this kind may be considered the theory of mixed Poisson processes, which was stimulated by its applications to sickness and accident statistics. Mixed Poisson processes were characterized either as the definite subclass of Markov processes, or as the simple point processes with the prescribed compensators. The family of the Hilbert space valued processes with independent increments and the related mixed exponential processes with given mixing distribution \(U\) are defined. Using their Markov property mixed exponential processes are characterized as semimartingales with prescribed triplets of predictable characteristics. Some examples and applications of this result are also considered.NEWLINENEWLINEFor the entire collection see [Zbl 0956.00022].