On the asymptotics of locally dependent point processes |
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Authors: | Aihua Xia Fuxi Zhang |
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Affiliation: | 1. Department of Mathematics and Statistics, The University of Melbourne, VIC 3010, Australia;2. School of Mathematical Sciences, Peking University, Beijing 100871, China |
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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. |
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