= Daniel T. Gillespie
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<Daniel T. Gillespie> developed stochastic simulation methods for reacting molecular populations. In the <Gillespie algorithm>, a <reaction propensity function> specifies an event rate, and the algorithm samples both the next reaction time and the reaction channel rather than evolving only mean concentrations.<Stochastic Simulation of Chemical Kinetics by Daniel T. Gillespie>[Stochastic chemical kinetics and exact simulation algorithm]{ref}
If the total propensity is $a_0>0$, the waiting time is exponentially distributed with rate $a_0$, and channel $j$ is selected with probability $a_j/a_0$ at the current state. His <tau-leaping> approach groups reaction events to accelerate simulation, introducing a controlled approximation rather than retaining the exact event-by-event law.<Approximate accelerated stochastic simulation of chemically reacting systems by Daniel T. Gillespie>[Leap condition and approximate grouped-reaction evolution]{ref}
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