Partial mean field limits in heterogeneous networks

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:129

Article

Chong, Carsten¹  Klueppelberg, Claudia¹ 

[1] Tech Univ Munich, Ctr Math Sci, Boltzmannstr 3, D-85748 Garching, Germany

关键词: Interacting particle system;    Interacting SDEs;    Heterogeneous networks;    Large deviations;    Law of large numbers;    Mean field theory;    Partial mean field system;    Preferential attachment;    Propagation of chaos;   

DOI  :  10.1016/j.spa.2018.12.018

来源: Elsevier

【 摘 要 】

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. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free