On the Maximum and Absorption Time of Left-Continuous Random Walk.

摘要

In a recent paper, P.J. Green obtained some conditional limit theorems for the absorption time of left-continuous random walk. His methods required certain distributions to have exponentially decreasing tails. Here a different approach is taken to produce Green's results under minimal conditions. Limit theorems are given for the maximum as the initial position of the random walk tends to infinity. (Author)