Corrected diffusion approximation for random walks conditioned to stay positive

Denis Denisov, Alexander Tarasov, Vitali Wachtel

Let $S_n$ be a random walk with i.i.d. increments which have zero mean and finite variance. For every $x\ge 0$ we define the stopping time ${\tau }_x:=\inf \{n\ge 1:x+S_n\le 0\}$ and conside…