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Many physical and biological processes are stochastic in nature.Computational models and simulations of such processes are a mathematical andcomputational challenge. The basic stochastic simulation algorithm waspublished by D. Gillespie about three decades ago [D.T. Gillespie, J. Phys.Chem. {\bf 81}, 2340, (1977)]. Since then, intensive work has been done to makethe algorithm more efficient in terms of running time. All accelerated versionsof the algorithm are aimed at minimizing the running time required to produce astochastic trajectory in state space. In these simulations, a necessarycondition for reliable statistics is averaging over a large number ofsimulations. In this study I present a new accelerating approach which does notalter the stochastic algorithm, but reduces the number of required runs. Byanalysis of collected data I demonstrate high precision levels with fewersimulations. Moreover, the suggested approach provides a good estimation ofstatistical error, which may serve as a tool for determining the number ofrequired runs.Comment: Accepted for publication at the Journal of Chemical Physics. 19  pages, including 2 Tables and 4 Figure

“All possible steps” approach to the accelerated use of Gillespie’s algorithm