  For Markov processes evolving on multiple time-scales a combination of large
component scalings and averaging of rapid fluctuations can lead to useful
limits for model approximation. A general approach to proving a law of large
numbers to a deterministic limit and a central limit theorem around it have
already been proven in [16] and [17]. We present here a general approach to
proving a large deviation principle in path space for such multi-scale Markov
processes. Motivated by models arising in systems biology, we apply these large
deviation results to general chemical reaction systems which exhibit multiple
time-scales, and provide explicit calculations for several relevant examples.
