For a number of processes in biology the appropriate stochastic modelling is done in
terms of multi-scale Markov processes with fully dependent slow and fast fluctuating variables.
The most common examples of such multi-scale processes are deterministic evolutions, jump-diffusions,
and state dependent Markov chains. The law of large numbers limit, central limit theorem,
and the corresponding large deviations behaviour of these models are all of interest in applications.
In this talk I will give a proof of the large deviations principle for such multi-scale systems,
and give an example of an intracellular reaction model on two time-scales for which these results apply.