A local limit theorem for random walk maxima with heavy tails
AbstractFor a random walk with negative mean and heavy-tailed increment distribution F, it is well known that under suitable subexponential assumptions, the distribution [pi] of the maximum has a tail [pi](x,[infinity]) which is asymptotically proportional to . We supplement here this by a local result showing that [pi](x,x+z] is asymptotically proportional to zF(x,[infinity]).
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Bibliographic InfoArticle provided by Elsevier in its journal Statistics & Probability Letters.
Volume (Year): 56 (2002)
Issue (Month): 4 (February)
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