Felix Hermann (Universität Freiburg)

Abstract:

We illustrate the interconnection between three classes of stochastic processes: As links between branching processes and random graphs frequently appear in the literature, we add to that a connection between birthdeath processes with disasters and duplication-based random graphs with edge deletion. For the third class of processes, i.e. a class of piecewise deterministic Markov processes we call p-jump processes, duality relations to a general class of branching processes with disasters as well as to duplication-based random graphs will be given. Via these relations, precise limit results we obtain for p-jump processes can be transferred to the other classes. Possible generalisations of these dualities will be discussed.