On Large Deviations of Markov Processes 1 with Discontinuous

This paper establishes a process-level large deviations principle for Markov processes in the Euclidean space with a discontinuity in the transition mechanism along a hyper-plane. The transition mechanism of the process is assumed to be continuous on one closed halfspace, and also continuous on the complementary open halfspace. Similar results were recently obtained for discrete time processes by Dupuis and Ellis and by Nagot. Our proof relies on the work of Blinovskii and Dobrushin, which in turn is based on an earlier work of Dupuis and Ellis. 2 Completed while a student at the University of Illinois, with partial support provided by a TUBITAK NATO Fellowship AMS 1991 subject classiications. Primary 60F10; secondary 60J. Abbreviated title. Large deviations with discontinuity.