Compound Poisson process approximation
نویسندگان
چکیده
Compound Poisson processes are often useful as approximate models, when describing the occurrence of rare events. In this paper, we develop a method for showing how close such approximations are. Our approach is to use Stein's method directly, rather than by way of declumping and a marked Poisson process; this has conceptual advantages, but entails technical difficulties. Several applications are given to illustrate the procedure. The Annals of Probability 2002, Vol. 30, No. 3, 1492–1537 COMPOUND POISSON PROCESS APPROXIMATION BY A. D. BARBOUR1 AND MARIANNE MÅNSSON2 Universität Zürich and Chalmers University of Technology Compound Poisson processes are often useful as approximate models, when describing the occurrence of rare events. In this paper, we develop a method for showing how close such approximations are. Our approach is to use Stein’s method directly, rather than by way of declumping and a marked Poisson process; this has conceptual advantages, but entails technical difficulties. Several applications are given to illustrate the procedure.
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