Equivalent Conditions of Asymptotics for the Density of the Supremum of a Random Walk in the Intermediate Case

Yuebao Wang () and Kaiyong Wang
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Yuebao Wang: Soochow University
Kaiyong Wang: Soochow University

Journal of Theoretical Probability, 2009, vol. 22, issue 2, 281-293

Abstract: Abstract This paper obtains some equivalent conditions about the asymptotics for the density of the supremum of a random walk with light-tailed increments in the intermediate case. To do this, the paper first corrects the proofs of some existing results about densities of random sums. On the basis of the above results, the paper obtains some equivalent conditions about the asymptotics for densities of ruin distributions in the intermediate case and densities of infinitely divisible distributions. In the above studies, some differences and relations between the results on a distribution and its corresponding density can be discovered.

Keywords: Random walk; Supremum; Random sum; Density; Ruin distribution; Infinitely divisible distribution; 60E07; 60F99 (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1007/s10959-009-0217-7

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