Strongly supermedian functions and optimal stopping

  title={Strongly supermedian functions and optimal stopping},
  author={Jean-François Mertens},
  journal={Zeitschrift f{\"u}r Wahrscheinlichkeitstheorie und Verwandte Gebiete},
  • J. Mertens
  • Published 1 June 1973
  • Mathematics
  • Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
Let E be the state space of a strong Markov process with semigroup Pt. Let f be a positive measurable function defined on E. The main problem we consider in this paper is the following optimal stopping problem: (1) Try to maximize E"(f(Xr)), where T ranges over the stopping times for the right continuous Markov process X, which has initial distribution # and semigroup Pt(2) What can you expect to get with such an optimal stopping? It is well known that a satisfactory answer to the second… 

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