TY - JOUR
T1 - Partial mean field limits in heterogeneous networks
AU - Chong, Carsten
AU - Klüppelberg, Claudia
N1 - Publisher Copyright:
© 2019 Elsevier B.V.
PY - 2019/12
Y1 - 2019/12
N2 - 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.
AB - 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.
KW - Heterogeneous networks
KW - Interacting SDEs
KW - Interacting particle system
KW - Large deviations
KW - Law of large numbers
KW - Mean field theory
KW - Partial mean field system
KW - Preferential attachment
KW - Propagation of chaos
UR - http://www.scopus.com/inward/record.url?scp=85060465431&partnerID=8YFLogxK
U2 - 10.1016/j.spa.2018.12.018
DO - 10.1016/j.spa.2018.12.018
M3 - Article
AN - SCOPUS:85060465431
SN - 0304-4149
VL - 129
SP - 4998
EP - 5036
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
IS - 12
ER -