Solving the Stein Equation in compound poisson approximation

Poisson Approximation and the Chen-Stein Method

The Chen-Stein method of Poisson approximation is a powerful tool for computing an error bound when approximating probabilities using the Poisson distribution. In many cases, this bound may be given in terms of first and second moments alone. We present a background of the method and state some fundamental Poisson approximation theorems. The body of this paper is an illustration, through varied...

Compound Poisson process approximation

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 a...

Stein-chen Method for Poisson Approximation

A Compound Poisson Approximation Inequality

We give conditions under which the number of events which occur in a sequence of m-dependent events is stochastically smaller than a suitably defined compound Poisson random variable. The results are applied to counts of sequence pattern appearances and to system reliability. We also provide a numerical example.

Third cumulant Stein approximation for Poisson stochastic integrals

We derive Edgeworth-type expansions for Poisson stochastic integrals, based on cumulant operators defined by the Malliavin calculus. As a consequence we obtain Stein approximation bounds for stochastic integrals, which are based on third cumulants instead of the L3 norm term found in the literature. The use of the third cumulant results into a convergence rate faster than the classical Berry-Es...