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

Author

Listed:
  • Yuebao Wang

    (Soochow University)

  • Hui Xu

    (Soochow University)

  • Dongya Cheng

    (Soochow University)

  • Changjun Yu

    (Nantong University)

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.

Suggested Citation

  • Yuebao Wang & Hui Xu & Dongya Cheng & Changjun Yu, 2018. "The local asymptotic estimation for the supremum of a random walk with generalized strong subexponential summands," Statistical Papers, Springer, vol. 59(1), pages 99-126, March.
    • Handle: RePEc:spr:stpapr:v:59:y:2018:i:1:d:10.1007_s00362-016-0754-y
    DOI: 10.1007/s00362-016-0754-y
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    References listed on IDEAS

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