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Asymptotics of the density of the supremum of a random walk with heavy-tailed increments. (English) Zbl 1120.60048

Summary: Under some relaxed conditions, we obtain some equivalent conditions on the asymptotics of the density of the supremum of a random walk with heavy-tailed increments. To do this, we investigate the asymptotics of the first ascending ladder height of a random walk with heavy-tailed increments. The results obtained improve and extend the corresponding classical results.

MSC:

60G50 Sums of independent random variables; random walks
60F99 Limit theorems in probability theory
60E05 Probability distributions: general theory
60G70 Extreme value theory; extremal stochastic processes
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