A Geometrical Characterization of the Multidimensional Hausdorff and Dale Polytopes with Applications to Exit Time Problems

We present formulae for the corner points of the multidimensional Hausdorff and Dale Polytopes and show how these results can be used to improve linear programming models for computing e. g. moments of exit distribution of diffusion processes. Specifically, we compute the mean exit time of twodimensional Brownian motion from the unit square and the unit triangle, as well as higher moments of the exit time of time space Brownian motion from a triangle