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A relation between moments of Liu process and Bernoulli numbers

Author

Listed:
  • Guanzhong Ma

    (Anyang Normal University)

  • Xiangfeng Yang

    (University of International Business and Economics)

  • Xiao Yao

    (Nankai University)

Abstract

This paper finds a relation between moments of Liu process and Bernoulli numbers. Firstly, by an exponential generating function of Bernoulli numbers, a useful integral formula is obtained. Secondly, based on this integral formula, the moments of a normal uncertain variable and Liu process are expressed via Bernoulli numbers.

Suggested Citation

  • Guanzhong Ma & Xiangfeng Yang & Xiao Yao, 2021. "A relation between moments of Liu process and Bernoulli numbers," Fuzzy Optimization and Decision Making, Springer, vol. 20(2), pages 261-272, June.
    • Handle: RePEc:spr:fuzodm:v:20:y:2021:i:2:d:10.1007_s10700-020-09338-5
    DOI: 10.1007/s10700-020-09338-5
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    References listed on IDEAS

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    1. Kai Yao & Baoding Liu, 2020. "Parameter estimation in uncertain differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 19(1), pages 1-12, March.
    2. Yang, Xiangfeng & Liu, Yuhan & Park, Gyei-Kark, 2020. "Parameter estimation of uncertain differential equation with application to financial market," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
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    Cited by:

    1. Gao, Yin & Gao, Jinwu & Yang, Xiangfeng, 2022. "Parameter estimation in uncertain delay differential equations via the method of moments," Applied Mathematics and Computation, Elsevier, vol. 431(C).
    2. Tang, Han & Yang, Xiangfeng, 2022. "Moment estimation in uncertain differential equations based on the Milstein scheme," Applied Mathematics and Computation, Elsevier, vol. 418(C).
    3. He, Liu & Zhu, Yuanguo, 2024. "Nonparametric estimation for uncertain fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    4. Liu He & Yuanguo Zhu & Ziqiang Lu, 2023. "Parameter estimation for uncertain fractional differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 22(1), pages 103-122, March.

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