%0 Journal Article %T Optimal stopping of strong Markov processes %A S£¿ren Christensen %A Paavo Salminen %A Bao Quoc Ta %J Mathematics %D 2012 %I arXiv %X We characterize the value function and the optimal stopping time for a large class of optimal stopping problems where the underlying process to be stopped is a fairly general Markov process. The main result is inspired by recent findings for L\'evy processes obtained essentially via the Wiener-Hopf factorization. The main ingredient in our approach is the representation of the $\beta$-excessive functions as expected suprema. A variety of examples is given. %U http://arxiv.org/abs/1203.4726v2