| Abstract: | Abstract Given a Markov process, we are interested in the numerical computation of the moments of the exit time from a bounded domain. We use a moment approach which, together with appropriate semidefinite positivity moment conditions, yields a sequence of semidefinite programs (or SDP relaxations), depending on the number of moments considered, that provide a sequence of nonincreasing (resp. nondecreasing) upper (resp. lower) bounds. The results are compared to the linear Hausdorff moment conditions approach considered for the LP relaxations in Helmes et al. Helmes, K., Röhl, S., Stockbridge, R.H. Computing moments of the exit time distribution for Markov processes by linear programming. Oper. Res. 2001, 49, 516–530]. The SDP relaxations are shown to be more general and more precise than the LP relaxations. |
