LAUSR

For Markov processes evolving on multiple time-scales a combination of large com- ponent 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 deter- ministic limit and a central limit theorem around it have already been proven in [15] and [16] for such multi-scale Markov processes. We present here a general approach to proving a large deviation principle in path space for such processes. Motivated by models with multiple time-scales arising in systems biology, we apply the large devia- tion results to general chemical reaction systems with explicit calculations for several relevant examples.