Distance estimates for dependent superpositions of point processes

Dominic Schuhmacher

Stochastic Processes and their Applications, 2005, vol. 115, issue 11, 1819-1837

Abstract: In this article, superpositions of possibly dependent point processes on a general space are considered. Using Stein's method for Poisson process approximation, an estimate is given for the Wasserstein distance d2 between the distribution of such a superposition and an appropriate Poisson process distribution. This estimate is compared to a modern version of Grigelionis' theorem, and to results of Banys [Lecture Notes in Statistics, vol. 2, Springer, New York, 1980, pp. 26-37], Arratia et al. [Ann. Probab. 17 (1989) 9-25] and Barbour et al. [Poisson Approximation, Oxford University Press, Oxford, 1992]. Furthermore, an application to a spatial birth-death model is presented.

Keywords: Point; processes; Poisson; process; approximation; Stein's; method; Superposition; Wasserstein; distance; Barbour-Brown; distance (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (3)

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