  Several different methods exist for efficient approximation of paths in
multiscale stochastic chemical systems. Another approach is to use bursts of
stochastic simulation to estimate the parameters of a stochastic differential
equation approximation of the paths. In this paper, multiscale methods for
approximating paths are used to formulate different strategies for estimating
the dynamics by diffusion processes. We then analyse how efficient and accurate
these methods are in a range of different scenarios, and compare their
respective advantages and disadvantages to other methods proposed to analyse
multiscale chemical networks.
