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Asymptotics of the density of the supremum of a random walk with heavy-tailed increments

Part of: Stochastic processes Distribution theory - Probability Limit theorems

Published online by Cambridge University Press:  14 July 2016

Yuebao Wang  and
Kaiyong Wang
Yuebao Wang*
Affiliation:
Soochow University
Kaiyong Wang*
Affiliation:
University of Science and Technology of Suzhou
*
∗Postal address: Department of Mathematics, Soochow University, Suzhou, 215006, P. R. China. Email address: ybwang@suda.edu.cn
∗∗Postal address: Department of Applied Mathematics, University of Science and Technology of Suzhou, Suzhou, 215009, P. R. China.
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Abstract

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Under some relaxed conditions, in this paper 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.

Keywords

Random walkheavy-tailed incrementfirst ascending ladder heightdensity of the supremumasymptotics

MSC classification

Primary: 60G50: Sums of independent random variables; random walks 60F99: None of the above, but in this section 60E05: Distributions
Type
Research Article
Information
Journal of Applied Probability , Volume 43 , Issue 3 , September 2006 , pp. 874 - 879
Copyright
© Applied Probability Trust 2006 

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