Once we have a graph labeled with transition rates, we can proceed to the master equation, which gives a deterministic law for how the stochastic state changes over time -- once an initial stochastic state is specified.

Let \\(\Gamma_{\sigma}(t)\\) be the stochastic state at time \\(t\\), given \\(\sigma\\) as the initial stochastic state.

Let \\(\Gamma_{\sigma}(t)\\) be the stochastic state at time \\(t\\), given \\(\sigma\\) as the initial stochastic state.