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A Functional Central Limit Theorem for SI processes On Configuration Model Graphs

KhudaBukhsh, W. R. ; Woroszylo, C. ; Rempala, G. A. ; Koeppl, H. (2017)
A Functional Central Limit Theorem for SI processes On Configuration Model Graphs.
In: Advances in Applied Probability, 54 (3)
doi: 10.1017/apr.2022.52
Artikel, Bibliographie

Kurzbeschreibung (Abstract)

We study a stochastic compartmental susceptible–infected (SI) epidemic process on a configuration model random graph with a given degree distribution over a finite time interval. We split the population of graph vertices into two compartments, namely, S and I, denoting susceptible and infected vertices, respectively. In addition to the sizes of these two compartments, we keep track of the counts of SI-edges (those connecting a susceptible and an infected vertex) and SS-edges (those connecting two susceptible vertices). We describe the dynamical process in terms of these counts and present a functional central limit theorem (FCLT) for them as the number of vertices in the random graph grows to infinity. The FCLT asserts that the counts, when appropriately scaled, converge weakly to a continuous Gaussian vector semimartingale process in the space of vector-valued càdlàg functions endowed with the Skorokhod topology. We discuss applications of the FCLT in percolation theory and in modelling the spread of computer viruses. We also provide simulation results illustrating the FCLT for some common degree distributions.

Typ des Eintrags: Artikel
Erschienen: 2017
Autor(en): KhudaBukhsh, W. R. ; Woroszylo, C. ; Rempala, G. A. ; Koeppl, H.
Art des Eintrags: Bibliographie
Titel: A Functional Central Limit Theorem for SI processes On Configuration Model Graphs
Sprache: Englisch
Publikationsjahr: 2017
Ort: Cambridge
Verlag: Cambridge University Press
Titel der Zeitschrift, Zeitung oder Schriftenreihe: Advances in Applied Probability
Jahrgang/Volume einer Zeitschrift: 54
(Heft-)Nummer: 3
DOI: 10.1017/apr.2022.52
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Kurzbeschreibung (Abstract):

We study a stochastic compartmental susceptible–infected (SI) epidemic process on a configuration model random graph with a given degree distribution over a finite time interval. We split the population of graph vertices into two compartments, namely, S and I, denoting susceptible and infected vertices, respectively. In addition to the sizes of these two compartments, we keep track of the counts of SI-edges (those connecting a susceptible and an infected vertex) and SS-edges (those connecting two susceptible vertices). We describe the dynamical process in terms of these counts and present a functional central limit theorem (FCLT) for them as the number of vertices in the random graph grows to infinity. The FCLT asserts that the counts, when appropriately scaled, converge weakly to a continuous Gaussian vector semimartingale process in the space of vector-valued càdlàg functions endowed with the Skorokhod topology. We discuss applications of the FCLT in percolation theory and in modelling the spread of computer viruses. We also provide simulation results illustrating the FCLT for some common degree distributions.

Freie Schlagworte: C3E
Fachbereich(e)/-gebiet(e): DFG-Sonderforschungsbereiche (inkl. Transregio)
DFG-Sonderforschungsbereiche (inkl. Transregio) > Sonderforschungsbereiche
DFG-Sonderforschungsbereiche (inkl. Transregio) > Sonderforschungsbereiche > SFB 1053: MAKI – Multi-Mechanismen-Adaption für das künftige Internet
DFG-Sonderforschungsbereiche (inkl. Transregio) > Sonderforschungsbereiche > SFB 1053: MAKI – Multi-Mechanismen-Adaption für das künftige Internet > C: Kommunikationsmechanismen
DFG-Sonderforschungsbereiche (inkl. Transregio) > Sonderforschungsbereiche > SFB 1053: MAKI – Multi-Mechanismen-Adaption für das künftige Internet > C: Kommunikationsmechanismen > Teilprojekt C3: Inhaltszentrische Sicht
Hinterlegungsdatum: 05 Apr 2017 22:44
Letzte Änderung: 20 Nov 2023 13:27
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