As with the Kubo's stochastic Liouville equation in hierarchal form, the counter n can go up to infinity which is a problem numerically, however Tanimura and Kubo provide a method by which the infinite hierarchy can be truncated to a finite set of N differential equations where N is determined by some constraint sensitive to the characteristics of the system i.e. frequency, amplitude of fluctuations, bath coupling etc. The "Terminator" defines the depth of the hierarchy. A simple relation to eliminate the ρ ρ ^ ^ n + 1 term is found. ρ ρ ^ ^ N + 1 = − − Θ Θ ^ ^ ρ ρ ^ ^ N / ℏ ℏ γ γ . With this terminator the hierarchy is closed at the depth N of the hierarchy by the final term: