A local limit theorem for random walk maxima with heavy tails

Søren Asmussen, Vladimir Kalashnikov, Dimitrios Konstantinides, Claudia Klüppelberg and Gurami Tsitsiashvili

Statistics & Probability Letters, 2002, vol. 56, issue 4, 399-404

Abstract: For 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]).

Keywords: Integrated; tail; Ladder; height; Subexponential; distribution (search for similar items in EconPapers)
Date: 2002
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Citations: View citations in EconPapers (12)

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