Before revision:  Our approach reduces the variance of the estimator by exploiting the positive correlation of these processes and improves the performance by skipping the propensity updates. Furthermore, by using propensity bounds to couple processes, our approach allows simultaneous perturbation of many reaction rates in computing the sensitivities, which further improves the efficiency of the estimator.
After revision:  For each simulation step, the nominal and perturbed processes under our coupling strategy are synchronized and often jump together, increasing their positive correlation and hence reducing the variance of the estimator. The distinctive feature of our approach in comparison with existing coupling approaches is that it only needs to maintain a single data structure storing propensity bounds of reactions during the simulation of the nominal and perturbed processes. Our approach allows to computing sensitivities of many reaction rates in computing the sensitivities, which further improves the efficiency of the estimator.