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This paper is concerned with elucidating a relationship between two commoncoupling methods for the continuous time Markov chain models utilized in thecell biology literature. The couplings considered here are primarily used in acomputational framework by providing reductions in variance for different MonteCarlo estimators, thereby allowing for significantly more accurate results fora fixed amount of computational time. Common applications of the couplingsinclude the estimation of parametric sensitivities via finite differencemethods and the estimation of expectations via multi-level Monte Carloalgorithms. While a number of coupling strategies have been proposed for themodels considered here, and a number of articles have experimentally comparedthe different strategies, to date there has been no mathematical analysisdescribing the connections between them. Such analyses are critical in order todetermine the best use for each. In the current paper, we show a connectionbetween the common reaction path (CRP) method and the split coupling (SC)method, which is termed coupled finite differences (CFD) in the parametricsensitivities literature. In particular, we show that the two couplings areboth limits of a third coupling strategy we call the "local-CRP" coupling, withthe split coupling method arising as a key parameter goes to infinity, and thecommon reaction path coupling arising as the same parameter goes to zero. Theanalysis helps explain why the split coupling method often provides a lowervariance than does the common reaction path method, a fact previously shownexperimentally.

An asymptotic relationship between coupling methods for stochastically modeled population processes