On dualities of random graphs and branching processes with disasters to Piecewise deterministic Markov processes

Abstract: 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 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 shown. Precise limit results we obtain for p-jump processes will be transferred to the other classes. Several possible generalisations of these dualities will be discussed.
Furthermore, limit results for degrees, cliques and star-like sub-graphs of the duplication graph model will be derived using martingale methods. Lastly, we outline an approach for the analysis of the sub-graph of non-isolated vertices via p-jump processes

Object Details

• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource
• Language: Englisch
• Notes: Universität Freiburg, Dissertation, 2019

Classification and Topics

• Keyword: Markov processes ; Random graphs ; Branching processes ; Jump processes ; Disasters ; Markov-Prozess ; Zufallsgraph ; Verzweigungsprozess

Contributors, Places and Time

• Event: Veröffentlichung
• (where): Freiburg
• (who): Universität
• (when): 2019
• Creator: Hermann, Felix
• Contributor: Pfaffelhuber, Peter ; Albert-Ludwigs-Universität Freiburg. Fakultät für Mathematik und Physik

Further information

• DOI: 10.6094/UNIFR/149193
• URN: urn:nbn:de:bsz:25-freidok-1491930
• Rights: Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Last update: 25.03.2025, 1:49 PM CET