Felix Hermann

Technische Universität Berlin | TUB ·  Workgroup Stochastics and Mathematical Finance

We study a random graph model in continuous time. Each vertex is partially copied with the same rate, i.e. an existing vertex is copied and every edge leading to the copied vertex is copied with independent probability p. In addition, every edge is deleted at constant rate, a mechanism which extends previous partial duplication models. In this mode...

A p-jump process is a piecewise deterministic Markov process with multiplicative jumps by a factor of p. We prove a limit theorem for such processes on the unit interval. Via duality with respect to probability generating functions, we deduce limiting results for the survival probabilities of time-homogeneous branching processes with arbitrary offs...

We study a random graph model in continuous time. Each vertex is partially copied with the same rate, i.e.\ an existing vertex is copied and every edge leading to the copied vertex is copied with independent probability $p$. In addition, every edge is deleted at constant rate, a mechanism which extends previous partial duplication models. In this m...

This thesis is based on 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 birth-death processes with disasters and duplication-based random graphs with edge deletion. For the third class of processes, i.e....

A $p$-jump process is a piecewise deterministic Markov process with jumps by a factor of $p$. We prove a limit theorem for such processes on the unit interval. Via duality with respect to probability generating functions, we deduce limiting results for the survival probabilities of time-homogeneous branching processes with arbitrary offspring distr...

We study the following model for an evolving random graph $\mathcal G = (G_n)_{n=n_0, n_0+1,...}$, where $G_n = (V_n, E_n)$ is a graph with $|V_n|=n$ vertices, $n=n_0,n_0+1,...$ In state $G_n = (V_n, E_n)$, a vertex $v\in V_n$ is chosen from $V_n$ uniformly at random and is $p$-copied. Upon such an event, a new vertex $v'\notin V_n$ is created and...