Year: 2011
Type: preprint
Abstract: Random events in space and time often exhibit a locally dependent structure. When the events are very rare and dependent structure is not too complicated, various studies in the literature have shown that Poisson and compound Poisson processes can provide adequate approximations. However, the accuracy of approximations does not improve or may even deteriorate when the mean number of events increases. In this paper, we investigate an alternative family of approximating point processes and establish Stein's method for their approximations. We prove two theorems to accommodate respectively the positively and negatively related dependent structures. Three examples are given to illustrate that our approach can circumvent the technical difficulties encountered in compound Poisson process approximation [see Barbour & Månsson (2002)] and our approximation error bound decreases when the mean number of the random events increases, in contrast to increasing bounds for compound Poisson process approximation.
Source: arXiv (Cornell University)
Authors: Xia, Aihua, Zhang, Fuxi
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2154942849