  The time-ordered product framework of quantum field theory can also be used
to understand salient phenomena in stochastic biochemical networks. It is used
here to derive Gillespie's Stochastic Simulation Algorithm (SSA) for chemical
reaction networks; consequently, the SSA can be interpreted in terms of Feynman
diagrams. It is also used here to derive other, more general simulation and
parameter-learning algorithms including simulation algorithms for networks of
stochastic reaction-like processes operating on parameterized objects, and also
hybrid stochastic reaction/differential equation models in which systems of
ordinary differential equations evolve the parameters of objects that can also
undergo stochastic reactions. Thus, the time-ordered product expansion (TOPE)
can be used systematically to derive simulation and parameter-fitting
algorithms for stochastic systems.
