Daniel T. Gillespie

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.^[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.^[ref]