Authors
Xiaowei Chen, Dan A Ralescu
Publication date
2013/12
Journal
Journal of Uncertainty Analysis and Applications
Volume
1
Pages
1-12
Publisher
Springer Berlin Heidelberg
Description
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.
Scholar articles
X Chen, DA Ralescu - Journal of Uncertainty Analysis and Applications, 2013