# Pathwise error bounds in Multiscale variable splitting methods for spatial stochastic kinetics Source: [Pathwise error bounds in Multiscale variable splitting methods for spatial stochastic kinetics]() Collection index: [llms.txt]() Data updated: 2026-06-05T05:01:01.279Z Authors: Augustin Chevallier, Stefan Engblom Published: 2016-07-04T09:59:14.000Z ## Abstract Stochastic computational models in the form of pure jump processes occur frequently in the description of chemical reactive processes, of ion channel dynamics, and of the spread of infections in populations. For spatially extended models, the computational complexity can be rather high such that approximate multiscale models are attractive alternatives. Within this framework some variables are described stochastically, while others are approximated with a macroscopic point value. We devise theoretical tools for analyzing the pathwise multiscale convergence of this type of variable splitting methods, aiming specifically at spatially extended models. Notably, the conditions we develop guarantee well-posedness of the approximations without requiring explicit assumptions of \\textit{a priori} bounded solutions. We are also able to quantify the effect of the different sources of errors, namely the \\emph{multiscale error} and the \\emph{splitting error}, respectively, by developing suitable error bounds. Computational experiments on selected problems serve to illustrate our findings. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()