The Annals of Probability

Some Poisson Approximations Using Compensators

Timothy C. Brown

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We give new results on the total variation distance of the distribution of a point process on the line from that of a Poisson process. Both one dimensional and function space distances are considered. Additionally similar bounds for marked point processes are given, both for the finite and infinite mark space cases. The bounds are all given in terms of the compensator of the point process (with respect to an arbitrary filtration) and are analogues and extensions of discrete time results of Freedman (1974) and Serfling (1975). Some new techniques for discrete approximation of compensators are used in the proofs. Examples of the use of the bounds appear elsewhere (Brown and Pollett, 1982, Brown, 1981), but an application to compound Poisson approximation and thinning of point processes is given here.

Article information

Ann. Probab., Volume 11, Number 3 (1983), 726-744.

First available in Project Euclid: 19 April 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 60G55: Point processes
Secondary: 60G44: Martingales with continuous parameter 60G07: General theory of processes

Point process marks Poisson process compensator discrete approximations


Brown, Timothy C. Some Poisson Approximations Using Compensators. Ann. Probab. 11 (1983), no. 3, 726--744. doi:10.1214/aop/1176993517.

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