  Parametric sensitivity analysis is a critical component in the study of
mathematical models of physical systems. Due to its simplicity, finite
difference methods are used extensively for this analysis in the study of
stochastically modeled reaction networks. Different coupling methods have been
proposed to build finite difference estimators, with the "split coupling," also
termed the "stacked coupling," yielding the lowest variance in the vast
majority of cases. Analytical results related to this coupling are sparse, and
include an analysis of the variance of the coupled processes under the
assumption of globally Lipschitz intensity functions [Anderson, SIAM Numerical
Analysis, Vol. 50, 2012]. Because of the global Lipschitz assumption utilized
in [Anderson, SIAM Numerical Analysis, Vol. 50, 2012], the main result there is
only applicable to a small percentage of the models found in the literature,
and it was conjectured that similar results should hold for a much wider class
of models. In this paper we demonstrate this conjecture to be true by proving
the variance of the coupled processes scales in the desired manner for a large
class of non-Lipschitz models. We further extend the analysis to allow for time
dependence in the parameters. In particular, binary systems with or without
time-dependent rate parameters, a class of models that accounts for the vast
majority of systems considered in the literature, satisfy the assumptions of
our theory.
