On the large deviation property of random measures on the $d$-dimensional Euclidean space
Commun. Korean Math. Soc. 2002 Vol. 17, No. 1, 71-80 Printed March 1, 2002
Dae Sik Hwang Air Force Academy
Abstract : We give a formulation of the large deviation property for rescalings of random measures on the $d$-dimensional Euclidean space $R^d$. The approach is global in the sense that the objects are Radon measures on $R^d$ and the dual objects are the continuous functions with compact support. This is applied to the cluster random measures with Poisson centers, a large class of random measures that includes the Poisson processes.
Keywords : large deviation property, random measure, Poisson point process, Poisson center cluster random measure