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
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Deutsche Nationalbibliothek Frankfurt am Main
- Umfang
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Online-Ressource
- Sprache
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Englisch
- Anmerkungen
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Universität Freiburg, Dissertation, 2019
- Schlagwort
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Markov processes
Random graphs
Branching processes
Jump processes
Disasters
Markov-Prozess
Zufallsgraph
Verzweigungsprozess
- Ereignis
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Veröffentlichung
- (wo)
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Freiburg
- (wer)
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Universität
- (wann)
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2019
- Urheber
- Beteiligte Personen und Organisationen
- DOI
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10.6094/UNIFR/149193
- URN
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urn:nbn:de:bsz:25-freidok-1491930
- Rechteinformation
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- Letzte Aktualisierung
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25.03.2025, 13:49 MEZ
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Beteiligte
Entstanden
- 2019