Integrated random walks conditioned to stay positive

Let $S(n)$ be a driftless random walk with finite variance. We consider an integrated random walk $A(n)=S(1)+S(2)+...+S(n)$. The main purpose of this talk is to discuss recent progress in studying the pair $(A(n),S(n))$ under condition that the integrated walk $A(k)$ remains positive up to a large time $n$.