Large Deviation Principle for Markov Chains in Continuous Time

Abstract

Let Yt be a homogeneous nonexplosive Markov process with generator R defined on a denumerable state space E (not necessarily ergodic). We introduce the empirical generator Gt of Yt 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.