Survival probability of a random walk

Question

I was looking for the probability that a discrete random walk stays below a certain level for $n$ steps. $x_0$ denotes the initial position and the position at the $i$-th step is $x_i=x_{i-1} + \eta_i$ where $\eta_i$ is a continouous and symmetric jump. I am interested in: $$q_n(x|y)=Pr[x_1 \leq y, \dots, x_{n-1} \leq y, y \leq x_n \leq x]$$ I know that for $y=0$ this is related to the well known Sparre-Andersen result. Are there any analytical results on this? Thanks in advance!