Abstract

Many problems in stochastic geometry can be formulated in terms of random measures. For example, additive nonnegative functionals of a point process are random measures. Associated with each random measure, there is a Palm measure. Assuming that the Palm measure and the random measure are defined on the same probability space, one can use the Campbell equation to construct a Stein identity and then use Stein's method to study probability approximations for the random measure. We will show how this is done in the case of normal approximation, Poisson approximation and Poisson process approximation. This talk is based on joint works with Aihua Xia and with Adrian Roellin and Aihua Xia.