Stiffness in stochastic chemically reacting systems: The implicit tau-leaping method

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Stochastic simulation of chemical kinetics. (2007, methodology): “To make it implicit by replacing x in the argument of the Poisson random variable with X(t+τ ), however, raises some serious questions in the context of Markov process theory, where updates are supposed to be past-forgetting; moreover, even if that replacement could be justified theoretically, there”
Stochastic approaches for modelling in vivo reactions (2004, methodology): “We discuss some further streamlining of the algorithm by Gibson and Bruck (2000), Gillespie (2001), Burrage and Tian (2003), Rathinam et al. (2003) and Tian and Burrage (2004a) leading to greater computational efficiency.”
A Dynamical Low-Rank Approach to the Chemical Master Equation (2008, methodology): “that many reaction events will occur without significantly changing the reaction propensities, allowing to locally approximate the inhomogenous Poisson process by a simpler distribution [17, 36, 7, 5].”
The finite state projection algorithm for the solution of the chemical master equation. (2006, methodology): “Algorithm [3, 2], tau-Leaping [5, 11 ], and various methods that have made quasi-steady state ap-”