Computing moments of the exit time distribution for Markov processes by linear programming

We provide a new approach to the numerical computation of moments of the exit time distribution of Markov processes. The method relies on a linear programming formulation of a process exiting from a bounded domain. The LP formulation characterizes the evolution of the process through the moments of the induced occupation measure and naturally provides upper and lower bounds for the exact values of the moments. The conditions the moments have to satisfy are derived directly from the generator of the Markov process and are not based on some approximation of the process. Excellent software is readily available because the computations involve infinite dimensional linear programs.