Asymptotic expansions for the distribution of the sojourn time of a random walk on a half-axis

A complete asymptotic expansion for $n\to\infty$ is obtained in a local limit theorem for the distribution of the sojourn time of a random walk with zero drift in the set $(b,\infty)$ during $n$ steps. Here $b=b(n)\to\infty$, $b(n)=o(n)$, and Cramér-type conditions are imposed on the distribution of jumps of the walk.