The local asymptotic estimation for the supremum of a random walk with generalized strong subexponential summands

Yuebao Wang (), Hui Xu, Dongya Cheng and Changjun Yu
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Yuebao Wang: Soochow University
Hui Xu: Soochow University
Dongya Cheng: Soochow University
Changjun Yu: Nantong University

Statistical Papers, 2018, vol. 59, issue 1, No 5, 99-126

Abstract: Abstract In this paper, the local asymptotic estimation for the supremum of a random walk and its applications are presented. The summands of the random walk have common long-tailed and generalized strong subexponential distribution. This distribution class and the corresponding generalized local subexponential distribution class are two new distribution classes with some good properties. Further, some long-tailed distributions with intuitive and concrete forms are found, which show that the intersection of the two above-mentioned distribution classes with long-tailed distribution class properly contain the strong subexponential distribution class and the locally subexponential distribution class, respectively.

Keywords: Random walk; Supremum; Local asymptotic estimation; Generalized strong subexponential distribution; Generalized locally subexponential distribution; Primary 60E05; Secondary 60F99 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s00362-016-0754-y

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