CENTRAL LIMIT THEOREMS AND DIFFUSION APPROXIMATIONS FOR MULTISCALE

Ordinary differential equations obtained as limits of Markov processes appear in many settings. They may arise by scaling large systems, or by av-eraging rapidly fluctuating systems, or in systems involving multiple time-scales, by a combination of the two. Motivated by models with multiple time-scales arising in systems biology, we present a general approach to proving a central limit theorem capturing the fluctuations of the original model around the deterministic limit. The central limit theorem provides a method for de-riving an appropriate diffusion (Langevin) approximation. 1. Introduction. Ther