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 |
| Zugehörige Links: | |
| 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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