  Let $S(n)$ be a centered random walk with finite second moment. We consider
the integrated random walk $T(n) = S(0)+S(1)+\dots+S(n)$. We prove invariance
principles for the meander and for the bridge of this process, under the
condition that the integrated random walk remains positive. Furthermore, we
prove the functional convergence of its Doob's $h$-transform to the
$h$-transform of the Kolmogorov diffusion conditioned to stay positive.
