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In this paper we study the well-know optimal stopping problem applied to a general family of continuous-time Markov process. The approach to follow is merely analytic and it is based on the characterization of stopping problems through the study of a certain variational inequality; namely one solution of this inequality will coincide with the optimal value of the stopping problem. In addition, by means of this characterization, it is possible to find the so-named continuation region, and as a byproduct obtaining the optimal stopping time. The most of the material is based on the semigroup theory, infinitesimal generators and resolvents. The chapter is a complete version of the former presentation without detailed proofs in [27].


Control Theory | Numerical Analysis and Computation


This is a post-peer-review, pre-copyedit version of a paper appearing in the Proceedings of the international workshop Modern Trends in Controlled Stochastic Processes: Theory and Applications. The final version is available online at: