Journal article
On the asymptotics of locally dependent point processes
A Xia, F Zhang
Stochastic Processes and their Applications | ELSEVIER SCIENCE BV | Published : 2012
Abstract
We investigate a family of approximating processes that can capture the asymptotic behaviour of locally dependent point processes. We prove two theorems presented to accommodate respectively the positively and negatively related dependent structures. Three examples are given to illustrate that our approximating processes can circumvent the technical difficulties encountered in compound Poisson process approximation (see Barbour and Månsson (2002) [10]) and our approximation error bound decreases when the mean number of the random events increases, in contrast to the increasing of bounds for compound Poisson process approximation. © 2012 Elsevier B.V. All rights reserved.
Grants
Awarded by University of Melbourne
Funding Acknowledgements
This work was supported by the Belz fund from the University of Melbourne (AX) and NSFC10901008 and the National Excellent Ph.D. Thesis fund 200722 from Peking University (FZ). We would like to thank Prof. A.D. Barbour for a suggestion leading to the example in Remark 4.2.