has characteristic has parameter approximate solution equation-free probabilistic steady-state approximation 2011-06-02 http://identifiers.org/doi/10.1063/1.2131050 AZ We present a probabilistic steady-state approximation that separates the time scales of an arbitrary reaction network, detects the convergence of a marginal distribution to a quasi-steady-state, directly samples the underlying distribution, and uses those samples to accurately predict the state of the system, including the effects of the slow dynamics, at future times. The numerical method produces an accurate solution of both the fast and slow reaction dynamics while, for stiff systems, reducing the computational time by orders of magnitude. The developed theory makes no approximations on the shape or form of the underlying steady-state distribution and only assumes that it is ergodic. <...> The developed theory may be applied to any type of kinetic Monte Carlo simulation to more efficiently simulate dynamically stiff systems, including existing exact, approximate, or hybrid stochastic simulation techniques. minimum fast/discrete reaction occurrences number number of samples maximum discrete number minimum fast rate accelerated stochastic simulation algorithm