Multivariate fractional phase–type distributions

We extend the Kulkarni class of multivariate phase–type distributions in a natural time–fractional way to construct a new class of multivariate distributions with heavy-tailed Mittag-Leffler(ML)-distributed marginals. The approach relies on assigning rewards to a non–Markovian jump process with ML sojourn times. This new class complements an earlier multivariate ML construction [2] and in contrast to the former also allows for tail dependence. We derive properties and characterizations of this class, and work out some special cases that lead to explicit density representations.

Robust stability of nonlinear piecewise deterministic systems under matching conditions

This paper deals with the robustness of the class of nonlinear piecewise deterministic systems with unknown but bounded uncertainties. Under the assumption that all the modes of the markovian jump process (disturbance) communicate, the complete access to the system state and the boundedness of the uncertainties, a sufficient condition for stochastic stability of this class of systems is given. An example is presented to validate the proposed results.