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- W2056842008 abstract "Let {S n ; n ≥ 0} be an asymptotically stable random walk and let M n denote it’s maximum in the first n steps. We show that the asymptotic behaviour of local probabilities for M n can be approximated by the density of the maximum of the corresponding stable process if and only if the renewal mass-function based on ascending ladder heights is regularly varying at infinity. We also give some conditions on the random walk, which guarantee the desired regularity of the renewal mass-function. Finally, we give an example of a random walk, for which the local limit theorem for M n does not hold." @default.
- W2056842008 created "2016-06-24" @default.
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- W2056842008 date "2010-10-09" @default.
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- W2056842008 title "Local limit theorem for the maximum of asymptotically stable random walks" @default.
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- W2056842008 doi "https://doi.org/10.1007/s00440-010-0326-3" @default.
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