Large deviations for Markov bridges with jumps

In this paper, we consider a family of Markov bridges with jumps constructed from truncated stable processes. These Markov bridges depend on a small parameter ħ > 0 , and have fixed initial and terminal positions. We propose a new method to prove a large deviation principle for this family of bridges based on compact level sets, change of measures, duality and various global and local estimates of transition densities for truncated stable processes.