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

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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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Acknowledgments

The authors are grateful to the two referees for their careful reading and valuable comments and suggestions, which greatly improve the original version of this paper. Research supported by the National Natural Science Foundation of China (No. 11071182 ), the National Natural Science Foundation of China (No. 11401415), the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (No. 13KJB110025).

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Authors and Affiliations

  1. School of Mathematical Sciences, Soochow University, Suzhou, 215006, China

    Yuebao Wang, Hui Xu & Dongya Cheng

  2. School of Sciences, Nantong University, Nantong, 226019, China

    Changjun Yu

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  1. Yuebao Wang
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  2. Hui Xu
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  3. Dongya Cheng
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  4. Changjun Yu
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Correspondence to Yuebao Wang.

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Wang, Y., Xu, H., Cheng, D. et al. The local asymptotic estimation for the supremum of a random walk with generalized strong subexponential summands. Stat Papers 59, 99–126 (2018). https://doi.org/10.1007/s00362-016-0754-y

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  • DOI: https://doi.org/10.1007/s00362-016-0754-y

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