A derived Markov process for modeling reaction networks

A reaction network arises when a set of reactants (chromosomes, chemicals, economic goods, or the like) recombine at specified rates to produce other reactants in the set. When the reactants are characterized in terms of "reactive regions" (schemata, active sites, building blocks), reaction networks can be modeled by classic stochastic urn models. The corresponding Markov processes are specified by matrices that, for realistic problems, are small enough to allow standard matrix operations and Monte Carlo estimates of important properties of the trajectory of the process, such as the expected time to first occurrence of some designated reactant.