  The molecular evolution in a gene regulatory network is classically modeled
by Markov jump processes. However, the direct simulation of such models is
extremely time consuming. Indeed, even the simplest Markovian model, such as
the production module of a single protein involves tens of variables and
biochemical reactions and an equivalent number of parameters. We study the
asymptotic behavior of multiscale sto- chastic gene networks using weak limits
of Markov jump processes. The results allow us to propose new models with
reduced execution times. In a new article, we have shown that, depending on the
time and concentration scales of the system, the Markov jump processes could be
approximated by piecewise deterministic processes. We give some applications of
our results for simple gene networks (Cook's model and Lambda-phage model).
