Convergence of the DCFTP-SSA for the first order reaction (12). (a) As a function of CPU time, we represent the Euclidean error ∊
of the stationary distribution of Eq. (12) with k = 5 sampled with the DCFTP-SSA (+) and with the standard SSA with stopping times T
= 2(○), 4(□), 6(◇). For this simple ME, the limiting value of the Euclidean error of the finite-time SSA is , where α = 1 - exp(-T
) and I0(x) is the modified Bessel function of the first kind . This means that SSA simulations that are run for a time T
will converge to a systematic sampling error, indicated by the dotted lines. This source of error is eliminated when using the DCFTP-SSA, which shows no flooring for ∊
and the expected N-1/2 scaling with the number of Monte Carlo samples . The guarantees provided by the DCFTP-SSA come at a modest computational cost, which is comparable to that of long SSA runs. (b) The distribution of coalescence times T
for the DCFTP-SSA is relatively symmetric and concentrated around the mean with a rapid decay for long times. The data presented corresponds to 6000 runs. This distribution reflects the benign structure of the unimodal stationary distribution of this particular ME, which makes long coalescence times unlikely.