Starting from the Langevin equation for a 1D Brownian particle, the mean square displacement (MSD) is calculated: $$\langle r^2 \rangle = \frac{2k_BT}{ζ}[t+τ_B(e^{-t/τ_B}-1)]$$ When $t\rightarrow \infty$, this expression shows that the MSD increases linearly with time. On the other hand, taking the limit for $t\rightarrow 0$ shows a quadratic dependence of MSD on time. This is a standard result from many textbooks and it is being referred to as the "ballistic" regime, where the particles are still under the effect of their initial speed/inertia.
This does not make much sense to me, since we have already made use of the equipartition theorem in order to extract this result, thus implying that the system is at equilibrium. Therefore, it is conceptually wrong to compute the limit for $t\rightarrow 0$ in the first place. Of course, since this is a standard result, it is probably me who is wrong. Can somebody explain in a more specific way what textbook writers mean when they refer to the "ballistic" regime of Brownian particles?