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.
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Acknowledgements
Guanzhong Ma was supported by the Key Project of Natural Science Foundation of Educational Committee of Henan Province (No. 20A110010). Xiangfeng Yang was supported by the Program for Young Excellent Talents in UIBE (No. 18YQ06). Xiao Yao was supported by National Natural Science Foundation of China (Grant No. 11901311) and the Fundamental Research Funds for the Central Universities, Nankai University (No. 63201148).
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Ma, G., Yang, X. & Yao, X. A relation between moments of Liu process and Bernoulli numbers. Fuzzy Optim Decis Making 20, 261–272 (2021). https://doi.org/10.1007/s10700-020-09338-5
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DOI: https://doi.org/10.1007/s10700-020-09338-5