Moments of the first descending epoch for a random walk with negative drift

Sergey Foss, Timofej Prasolov

We consider the first exit time $\tau =\min \{n\ge 1:S_n\le 0\}$ from the positive halfline of a random walk $S_n={\sum }_1^n{\xi }_i,n\ge 1$ with i.d.d. summands having a negative drif…