A numerical method for solving uncertain differential equations

By Kai Yao, Xiaowei Chen. Journal of Intelligent & Fuzzy Systems, 2013

387 citations recorded by the source corpus.

Subfields: Applied Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/ac52ae124ffa2992ce7a16d1851a81476ae435d3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Yuanguo Zhu
2. Yuan Gao
3. Baoding Liu
4. Kai Yao
5. Xiangfeng Yang
6. Dan A. Ralescu
7. Jiajun Sun
8. Jinwu Gao

In Statistics and Probability

1. Yuanguo Zhu
2. Kai Yao
3. Xiangfeng Yang
4. Baoding Liu
5. Xiaowei Chen
6. Jiajun Sun
7. Yuan Gao
8. Dan A. Ralescu

Citations in the corpus

• Liu process and uncertain calculus (2013, methodology): “(Yao-Chen Formula [20]) Let Xt and X t be the solution and α-path of the uncertain differential equation dXt = f (t,Xt)dt + g(t,Xt)dCt , respectively.”
• Existence and uniqueness of the solution to uncertain fractional differential equation (2015, methodology): “An existence and uniqueness theorem of solution for the uncertain differential equation (1) was proved by Chen and Liu [21].”
• Extreme values and integral of solution of uncertain differential equation (2013, methodology): “Then Yao and Chen [17] proposed a numerical method for solving uncertain differential equation.”
• Bang-bang control model for uncertain switched systems (2015, neutral): “Definition 6 (Yao and Chen [21]).”
• Uncertain differential games with application to capitalism (2013, methodology): “Chen and Ralescu [18] defined and discussed the Liu process and uncertain calculus.”
• Runge-Kutta Method for Solving Uncertain Differential Equations (2015, background): “(Yao and Chen [19]) Let Xt and Xαt be the solution and α-path of the uncertain differential equation dXt = f (t,Xt) dt + g (t,Xt) dCt .”
• A type of uncertain differential equations with analytic solution (2013, methodology): “In addition, some numerical methods were designed to calculate the uncertainty distributions of the solution and the extreme values of the solution by Yao and Chen [26] and Yao [27].”
• Geometric Average Asian Option Pricing for Uncertain Financial Market (2014, background): “2 ([14]) Let α be a number with 0 < α < 1.”
• Asian Option Pricing Formula for Uncertain Financial Market (2015, methodology): “Yao and Chen [23] introduced the 99-method which is a numerical method for uncertain differential equations.”
• Existence and Uniqueness Theorem on Uncertain Dierential Equations with Local Lipschitz Condition (2012, positive): “For this UDE, Chen and Liu's existence and uniqueness theorem does not work.”
• Toward uncertain finance theory (2013, methodology): “This result is called the Yao-Chen formula [8].”