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SUMMARY:Function central limit theorem for Susceptible-Infected process on
configuration model graphs: Further insights into the accuracy of the cor
relation equations
DTSTART;VALUE=DATE-TIME:20180711T010000Z
DTEND;VALUE=DATE-TIME:20180711T013000Z
DTSTAMP;VALUE=DATE-TIME:20241107T231641Z
UID:indico-contribution-16@conferences.maths.unsw.edu.au
DESCRIPTION:Speakers: Wasiur Rahman Khuda Bukhsh (Technische Universität
Darmstadt)\nWe 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 grap
h nodes into two compartments\, namely\, S and I\, denoting susceptible an
d infected nodes\, respectively. In addition to the sizes of these two com
partments\, we study counts of SI-edges (those connecting a susceptible an
d an infected node)\, and SS-edges (those connecting two susceptible nodes
). We describe the dynamical process in terms of these counts and present
a functional central limit theorem (FCLT) for them when the number of node
s in the random graph grows to infinity. To be precise\, we show that thes
e counts\, when appropriately scaled\, converge weakly to a continuous Gau
ssian vector semimartingale process in the space of vector-valued càdlàg
functions endowed with the Skorohod topology. Based on the results obtain
ed\, we further investigate the accuracy of the so-called correlation equa
tions from ecology literature. We show that for a certain class of degree
distributions\, called Poisson-type (PT) distributions\, the pair approxim
ation approach is exact in the sense that it correctly estimates the limit
ing first order moments of the various count variables.\n\nhttps://confere
nces.maths.unsw.edu.au/event/2/contributions/16/
LOCATION:University of Sydney New Law School/--026
URL:https://conferences.maths.unsw.edu.au/event/2/contributions/16/
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