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

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

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

Ereignis
Veröffentlichung
(wo)
Freiburg
(wer)
Universität
(wann)
2019
Urheber
Beteiligte Personen und Organisationen

DOI
10.6094/UNIFR/149193
URN
urn:nbn:de:bsz:25-freidok-1491930
Rechteinformation
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Letzte Aktualisierung
25.03.2025, 13:49 MEZ

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Entstanden

  • 2019

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