Optimal stopping of strong Markov processes
  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. 
S\"oren Christensen, Paavo Salminen and Bao Quoc Ta
math.PR