Estimating parametric sensitivity of observables at stationary states of stochastic dynamics is computationally a difficult task due to large variance of standard estimators developed for finite time horizon problems. We present new, low variance estimators developed for stationary sensitivity. To accelerate stationary averaging in stochastic reaction networks that exhibit metastability or rare events we present parallel replica dynamics for continuous time Markov chains. We demonstrate that the proposed method accelerates stationary distribution sampling and yields correct stationary averages. Combined with the new estimators for stationary sensitivity it yields an efficient computational method for sensitivity analysis in systems with strong metastability. Furthermore, we show that it can be combined with path-space information bounds on path-dependent functionals. Such bounds provide error estimates on quantities of interest as well as bounds on parametric sensitivity in complex reaction networks.We also present computational examples demonstrating performance of the parallel implementation.
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