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Towards Automatic Global Error Control: Computable Weak Error Expansion for the Tau-Leap Method
This work develops novel error expansions with computable leading order terms
for the global weak error in the tau-leap discretization of pure jump processes
arising in kinetic Monte Carlo models. Accurate computable a posteriori error
approximations are the basis for adaptive algorithms; a fundamental tool for
numerical simulation of both deterministic and stochastic dynamical systems.
These pure jump processes are simulated either by the tau-leap method, or by
exact simulation, also referred to as dynamic Monte Carlo, the Gillespie
algorithm or the Stochastic simulation algorithm. Two types of estimates are
presented: an a priori estimate for the relative error that gives a comparison
between the work for the two methods depending on the propensity regime, and an
a posteriori estimate with computable leading order term