On asymptotic equivalence among the solutions of some defective renewal equations

Gao, Qingwu; Liu, Yu; Psarrakos, Georgios; Wang, Yuebao

doi:10.1007/s10986-013-9216-6

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

Wang¹,

Xu²,

Cheng³

et al. 2016

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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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