Application of martingale methods to a change set problem

Abstract

A collection of random points in a bounded rectangle [0, R] 2 of the positive quadrant changes its intensity on an unobservable random set xi. The goal is to detect the random change set in an optimal way, according to some reward function. Given the change set, the random points are assumed to be distributed according to a Poisson process N with intensities mu0 on xic and mu1 on xi. Optimal solutions are found for various reward functions and applied to some examples.