Partial mean field limits in heterogeneous networks

Carsten Chong, Claudia Klüppelberg

Publikation: Beitrag in FachzeitschriftArtikelBegutachtung

2 Zitate (Scopus)

Abstract

We investigate systems of interacting stochastic differential equations with two kinds of heterogeneity: one originating from different weights of the linkages, and one concerning their asymptotic relevance when the system becomes large. To capture these effects, we define a partial mean field system, and prove a law of large numbers with explicit bounds on the mean squared error. Furthermore, a large deviation result is established under reasonable assumptions. The theory will be illustrated by several examples: on the one hand, we recover the classical results of chaos propagation for homogeneous systems, and on the other hand, we demonstrate the validity of our assumptions for quite general heterogeneous networks including those arising from preferential attachment random graph models.

OriginalspracheEnglisch
Seiten (von - bis)4998-5036
Seitenumfang39
FachzeitschriftStochastic Processes and their Applications
Jahrgang129
Ausgabenummer12
DOIs
PublikationsstatusVeröffentlicht - Dez. 2019

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