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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.
A novel class of implicit Milstein type methods is devised and analyzed in the present work for stochastic differential equations (SDEs) with non-globally Lipschitz drift and diffusion coefficients. By incorporating a pair of method parameters $theta
We introduce a hybrid method to couple continuous Galerkin finite element methods and high-order finite difference methods in a nonconforming multiblock fashion. The aim is to optimize computational efficiency when complex geometries are present. The
We present a hybridization technique for summation-by-parts finite difference methods with weak enforcement of interface and boundary conditions for second order, linear elliptic partial differential equations. The method is based on techniques from
Reaction networks are often used to model interacting species in fields such as biochemistry and ecology. When the counts of the species are sufficiently large, the dynamics of their concentrations are typically modeled via a system of differential e
The stable operation of gas networks is an important optimization target. While for this task commonly finite volume methods are used, we introduce a new finite difference approach. With a summation by part formulation for the spatial discretization,