  In the presence of multiscale dynamics in a reaction network, direct
simulation methods become inefficient as they can only advance the system on
the smallest scale. This work presents stochastic averaging techniques to
accelerate computations for obtaining estimates of expected values and
sensitivities with respect to the steady state distribution. A two-time-scale
formulation is used to establish bounds on the bias induced by the averaging
method. Further, this formulation provides a framework to create an accelerated
`averaged' version of most single-scale sensitivity estimation method. In
particular, we propose a new lower-variance ergodic likelihood ratio type
estimator for steady-state estimation and show how one can adapt it to
accelerated simulations of multiscale systems.Lastly, we develop an adaptive
"batch-means" stopping rule for determining when to terminate the
micro-equilibration process.
