Liu process and uncertain calculus

By Xiaowei Chen, Dan A. Ralescu. 2013

117 citations recorded by the source corpus.

Uncertain calculus is a branch of mathematics that deals with the integral and differential of functions of uncertain processes. This paper first introduces the Liu process as an uncertain process defined by the Liu integral. Some properties of Liu processes are investigated such as sample continuity property, finite variation property, and the fact that a continuously differentiable function of the Liu process is another Liu process, among others. Based on the Liu process, the uncertain integral is extended. Furthermore, some mathematical properties are proved, including the fundamental theorem, change of variable theorem, and integration by parts theorem. Finally, uncertain calculus with respect to multiple Liu processes is discussed.

Subfields: Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e9ea4913eb9f963d1b95e844566b73d29320bb49

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In Management Science and Operations Research

1. Kai Yao
2. Yongchao Hou
3. Xiangfeng Yang
4. Yuanyuan Shen
5. Jinwu Gao
6. Baoding Liu
7. Yuanguo Zhu
8. Xiaowei Chen

In Statistics and Probability

1. Kai Yao
2. Xiangfeng Yang
3. Baoding Liu
4. Yuanyuan Shen
5. Jinwu Gao
6. Yongchao Hou
7. Yuanguo Zhu
8. Xiaowei Chen

Citations in the corpus

• Extreme values and integral of solution of uncertain differential equation (2013, background): “Besides, Chen and Ralescu [12] founded uncertain calculus with respect to general Liu process.”
• A type of uncertain differential equations with analytic solution (2013, background): “After that, Chen and Ralescu [13] proposed an uncertain integral with respect to the general Liu process.”
• Uncertain differential games with application to capitalism (2013, background): “Chen, X, Ralescu, DA: Liu process and uncertain calculus.”
• Subadditivity of chance measure (2014, background): “In addition, an uncertain integral was proposed by Chen and Ralescu [10] presented with respect to the general Liu process.”
• Runge-Kutta Method for Solving Uncertain Differential Equations (2015, background): “(Chen and Ralescu [21]) Let Zt be an uncertain process and let Ct be a canonical Liu process.”
• Toward uncertain finance theory (2013, background): “Chen, XW, Liu, YH, Ralescu, DA: Uncertain stock model with periodic dividends.”