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

Angaben zum Objekt

• Standort: Deutsche Nationalbibliothek Frankfurt am Main
• Umfang: Online-Ressource
• Sprache: Englisch
• Anmerkungen: Universität Freiburg, Dissertation, 2019

Klassifikation und Themen

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

Beteiligte, Orts- und Zeitangaben

• Ereignis: Veröffentlichung
• (wo): Freiburg
• (wer): Universität
• (wann): 2019
• Urheber: Hermann, Felix
• Beteiligte Personen und Organisationen: Pfaffelhuber, Peter ; Albert-Ludwigs-Universität Freiburg. Fakultät für Mathematik und Physik

Weitere Informationen

• DOI: 10.6094/UNIFR/149193
• URN: urn:nbn:de:bsz:25-freidok-1491930
• Rechteinformation: Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Letzte Aktualisierung: 25.03.2025, 13:49 MEZ