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Variation analysis of uncertain stationary independent increment processes

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  • Chen, Xiaowei

Abstract

A stationary independent increment process is an uncertain process with stationary and independent increments. This paper aims to calculate the variance of stationary independent increment processes, and gains that, for each fixed time, the variance is a constant multiplying the square of time. Based on this result, it is proved that the total variation of stationary independent increment process with finite variance is bounded almost surely. Besides, the quadratic variation of stationary independent increment process with finite variance is 0 almost surely and in mean.

Suggested Citation

  • Chen, Xiaowei, 2012. "Variation analysis of uncertain stationary independent increment processes," European Journal of Operational Research, Elsevier, vol. 222(2), pages 312-316.
    • Handle: RePEc:eee:ejores:v:222:y:2012:i:2:p:312-316
    DOI: 10.1016/j.ejor.2012.05.010
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    Cited by:

    1. Lihua Sun & Junpeng Guo & Yanlin Zhu, 2020. "A multi-aspect user-interest model based on sentiment analysis and uncertainty theory for recommender systems," Electronic Commerce Research, Springer, vol. 20(4), pages 857-882, December.
    2. Xiaoxia Huang & Liying Song, 2018. "An emergency logistics distribution routing model for unexpected events," Annals of Operations Research, Springer, vol. 269(1), pages 223-239, October.
    3. Liu, Yang & Zhang, Xingfang & Ma, Weimin, 2017. "A new uncertain insurance model with variational lower limit," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 164-169.
    4. Jian Zhou & Yujiao Jiang & Athanasios A. Pantelous & Weiwen Dai, 2023. "A systematic review of uncertainty theory with the use of scientometrical method," Fuzzy Optimization and Decision Making, Springer, vol. 22(3), pages 463-518, September.
    5. Sheng, Yuhong & Yao, Kai & Qin, Zhongfeng, 2020. "Continuity and variation analysis of fractional uncertain processes," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).

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