On the maximum and absorption time of left-continuous random walk
- 1 June 1978
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 15 (2) , 292-299
- https://doi.org/10.2307/3213402
Abstract
In a recent paper Green (1976) obtained some conditional limit theorems for the absorption time of left-continuous random walk. His methods require that in the driftless case the increment distribution has exponentially decreasing tails and that the same is true for a transformed distribution in the case of negative drift. Here we take a different approach which will 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.Keywords
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