Large Deviation Principle for Markov Chains in Continuous Time

Let $Y_t$ be a homogeneous nonexplosive Markov process with generator $R$ defined on a denumerable state space $E$ (not necessarily ergodic). We introduce the empirical generator $G_t$ of $Y_t$ and prove the Ruelle–Lanford property, which implies the weak LDP. In a fairly broad setting, we show how to perform almost all classical operations (e.g., contraction) on the weak LDP under suitable assumptions, whence Sanov's theorem follows.