Fast Probability Generating Function Method for Stochastic Chemical Reaction Networks

Chemical master equations of the stochastic reaction network can be reformulated into a partial differential equation(PDE) of a probability generating function (PGF). Such PDEs are mostly hard to deal with due to variable coefficients and lack of proper boundary conditions. In this paper, we propose a way to reduce PGF-PDEs into a sparse linear system of coefficients of a power series solution. A power of such matrix gives a fast approximation of the solution. The process can be further accelerated by truncating high-order moments. The truncation also makes the method applicable to reaction networks with time-varying reaction rates. We show numerical accuracy of the method by simulating motivating biochemical examples including a viral infection model and G(2)/M model.