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Some Poisson approximations using compensators. (English) Zbl 0551.60048

The distance between a Poisson and another point process may appropriately be measured by certain norms on the difference between the compensators of the two processes. Bounds on the distance between the random processes are derived here in terms of such norms involving the respective compensators; these extend earlier discrete-time results of D. Freedman [ibid. 2, 256-269 (1974; Zbl 0301.60021)] and R. J. Serfling [ibid. 3, 726-731 (1975; Zbl 0321.60018)]. Similar bounds are found for marked point processes. New techniques for discrete approximation of compensators are used in the proofs. Applications to compound Poisson approximations and thinning of point processes are provided.
Reviewer: F.J.Beutler

MSC:

60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
60G44 Martingales with continuous parameter
60G07 General theory of stochastic processes
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