arXiv subjects

D. P. Lyberopoulos

Publications and source records attributed to D. P. Lyberopoulos.

3 recordsLinked to original sources

arXiv2016

On the equivalence of various definitions of mixed Poisson processes

Under mild assumptions the equivalence of the mixed Poisson process with mixing parameter a real-valued random variable to the one with mixing distribution as well as to the mixed Poisson process in the sense of Huang is obtained, and a characterization of each one of the above mixed Poisson processes in terms of disintegrations is provided. Moreover, some examples of "canonical" probability spaces admitting counting processes satisfying the equivalence of all above statements are given. Finally, it is shown that our assumptions are essential for the characterization of mixed Poisson processes in terms of disintegrations.

math.PR↗

arXiv2014

Some Characterizations Of Mixed Renewal Processes

Some characterizations of mixed renewal processes in terms of exchangeability and of different types of disintegrations are given. As a consequence, an existence result for mixed renewal processes, providing also a new construction for them, is obtained. As an application, some concrete examples of constructing such processes are presented and the corresponding disintegrating measures are explicitly computed.

math.PR↗

arXiv2012

Some Characterizations of Mixed Poisson Processes

A characterization of mixed Poisson processes in terms of disintegrations is proven. As a consequence some further characterizations of such processes via claim interarrival processes, martingales and claim measures are obtained. Some revisions are required

math.PR↗