On large deviations of Markov processes with discontinuous statistics (Q1296616)

The authors establish a large deviations principle for a Markov random process in \(\mathbb{R}^d\) with \(d\) discontinuities in the transition mechanism along a hyperplane. The transition mechanism of the process is assumed to be continuous on one closed half-space, and also continuous on the complementary open half-space. The proof of the presented result relies on the work of \textit{V. M. Blinovskij} and \textit{R. L. Dobrushin} [in: The Dynkin Festschrift: Markov processes and their applications. Prog. Probab. 34, 1-59 (1994; Zbl 0819.60029)].