Monotone stopping rules for stochastic processes in a semimartingale representation with applications

A monotone stopping problem is considered for stochastic processes in a semimartingale representation. Such a representation allows a direct infinitesimal characterization of the optimal stopping time. Transformations of such processes are investigated which leave the semimartingale property unchanged. One of these transformations is a change of filtration which leads to the stopping problem with partial information. Finally an application is discussed.