Fig. 1.

Five sample paths for the simple birth-death process are plotted along with the exponential growth model $m\left(t\right)=3e^{0.1t}$. Three sample paths have finite time to extinction, whereas two sample paths approach infinity. Close-ups of the sample paths are graphed to time 20 on the right. Parameter values are $B=1.1$ and $D=1$, with initial condition $X\left(0\right)=3$. For the simple birth-death process, probability of extinction is ${\mathrm{\mathbb{P}}}_{\text{ext}}={\left(D/B\right)}^3=0.751$ and the mean and the standard deviation for time to extinction, conditioned on extinction, are $\mu =5.34$ and $\sigma =6.71$.