@TechReport{ it:2008-020,
author = {Stefan Engblom},
title = {Parallel in Time Simulation of Multiscale Stochastic
Chemical Kinetics},
institution = {Department of Information Technology, Uppsala University},
department = {Division of Scientific Computing},
year = {2008},
number = {2008-020},
month = aug,
note = {Extended abstract to appear in Proceedings of ICNAAM
2008},
abstract = {A version of the time-parallel algorithm parareal is
analyzed and applied to stochastic models in chemical
kinetics. A fast predictor at the macroscopic scale
(evaluated in serial) is available in the form of the usual
reaction rate equations. A stochastic simulation algorithm
is used to obtain an exact realization of the process at
the mesoscopic scale (in parallel).
The underlying stochastic description is a jump process
driven by the Poisson measure. A convergence result in this
arguably difficult setting is established suggesting that a
homogenization of the solution is advantageous. We devise a
simple but highly general such technique.
Three numerical experiments on models representative to the
field of computational systems biology illustrate the
method. For non-stiff problems, it is shown that the method
is able to quickly converge even when stochastic effects
are present. For stiff problems we are instead able to
obtain fast convergence 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 stochastic ones. This construction
is clearly possible to apply also to stochastic models
within other fields. }
}