Compound Poisson process approximation

Compound Poisson process approximation

A. D. Barbour and Marianne Månsson

Source: Ann. Probab. Volume 30, Number 3 (2002), 1492-1537.

Abstract

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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Primary Subjects: 60G55, 62E17

Secondary Subjects: 60F05

Keywords: Extreme values; point processes; compound Poisson process; Stein's method

Full-text: Open access

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aop/1029867135
Digital Object Identifier: doi:10.1214/aop/1029867135
Mathematical Reviews number (MathSciNet): MR1920275
Zentralblatt MATH identifier: 1033.60059

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