  Many biochemical systems appearing in applications have a multiscale
structure so that they converge to piecewise deterministic Markov processes in
a thermodynamic limit. The statistics of the piecewise deterministic process
can be obtained much more efficiently than those of the exact process. We
explore the possibility of coupling sample paths of the exact model to the
piecewise deterministic process in order to reduce the variance of their
difference. We then apply this coupling to reduce the computational complexity
of a Monte Carlo estimator. In addition to rigorous results concerning the
asymptotic computational complexity of the Monte Carlo estimator, numerical
simulations are performed on some simple biological models confirming that
computational gains are made.
