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

2014/06/12 by Yuebao Wang, Wang, Yuebao, Hui Xu +5
Decision Sciences · Mathematics · #60E05 #60F99 #FOS: Mathematics #Mathematical Approximation and Integration #Probability (math.PR) #Probability and Risk Models #Statistical Distribution Estimation and Applications #math.PR #msc:60E05 #msc:60F99

paper · pdf · doi:10.48550/arxiv.1406.3234

26 pages

openalex publication_date 2014/06/12 · arxiv created 2016/02/16 · arxiv updated 2016/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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