The Stein-Chen Method, Point Processes and Compensators

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...

Stein-chen Method for Poisson Approximation

The Stein and Chen-Stein methods for functionals of non-symmetric Bernoulli processes

Based on a new multiplication formula for discrete multiple stochastic integrals with respect to non-symmetric Bernoulli random walks, we extend the results of [14] on the Gaussian approximation of symmetric Rademacher sequences to the setting of possibly non-identically distributed independent Bernoulli sequences. We also provide Poisson approximation results for these sequences, by following ...

Two Moments Suffice for Poisson Approximations: the Chen-stein Method

Convergence to the Poisson distribution, for the number of occurrences of dependent events, can often be established by computing only first and second moments, but not higher ones. This remarkable result is due to Chen (1975). The method also provides an upper bound on the total variation distance to the Poisson distribution, and succeeds in cases where third and higher moments blow up. This p...

On Using the First Difference in Stein - Chen Method

This paper investigates an alternative way of using the Stein-Chen method in Poisson approximations. There are three principal bounds stated in terms of reduced Palm probabilities for general point processes. The rst two are for the accuracy of Poisson random variable approximation to the distribution of the number of points in a point process with respect to the total variation metric and Wass...