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A version of the time-parallel algorithm parareal is analyzed and applied tostochastic models in chemical kinetics. A fast predictor at the macroscopicscale (evaluated in serial) is available in the form of the usual reaction rateequations. A stochastic simulation algorithm is used to obtain an exactrealization of the process at the mesoscopic scale (in parallel).  The underlying stochastic description is a jump process driven by the Poissonmeasure. A convergence result in this arguably difficult setting is establishedsuggesting that a homogenization of the solution is advantageous. We devise asimple but highly general such technique.  Three numerical experiments on models representative to the field ofcomputational systems biology illustrate the method. For non-stiff problems, itis shown that the method is able to quickly converge even when stochasticeffects are present. For stiff problems we are instead able to obtain fastconvergence to a homogenized solution.  Overall, the method builds an attractive bridge between on the one hand,macroscopic deterministic scales and, on the other hand, mesoscopic stochasticones. This construction is clearly possible to apply also to stochastic modelswithin other fields.

Parallel in Time Simulation of Multiscale Stochastic Chemical Kinetics