Open Access
August, 1983 Some Poisson Approximations Using Compensators
Timothy C. Brown
Ann. Probab. 11(3): 726-744 (August, 1983). DOI: 10.1214/aop/1176993517


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.


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Timothy C. Brown. "Some Poisson Approximations Using Compensators." Ann. Probab. 11 (3) 726 - 744, August, 1983.


Published: August, 1983
First available in Project Euclid: 19 April 2007

zbMATH: 0551.60048
MathSciNet: MR704559
Digital Object Identifier: 10.1214/aop/1176993517

Primary: 60G55
Secondary: 60G07 , 60G44

Keywords: compensator , discrete approximations , marks , point process , Poisson process

Rights: Copyright © 1983 Institute of Mathematical Statistics

Vol.11 • No. 3 • August, 1983
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