Existence and uniqueness theorem for uncertain differential equations

By Xiaowei Chen, Baoding Liu. Fuzzy Optimization and Decision Making, 2010

497 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d74a3b4016ce24384a6b949017d50a1ced2a8257

How researchers see this paper

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

In Control and Systems Engineering

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

In Management Science and Operations Research

1. Kai Yao
2. Yuanguo Zhu
3. Jin Peng
4. Xiangfeng Yang
5. Xiaowei Chen
6. Baoding Liu
7. Yuanyuan Shen
8. Dan A. Ralescu

In Statistics and Probability

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

Citations in the corpus

• A type of uncertain differential equations with analytic solution (2013, background): “Then Chen and Liu [15] gave a sufficient condition for an uncertain differential equation having a unique solution.”
• A numerical method for solving uncertain differential equations (2013, methodology): “It has been proved by Chen and Liu [1] that the linear uncertain differential equation dXt = (u1tXt + u2t)dt + (v1tXt + v2t)dCt”
• Uncertain models for single facility location problems on networks (2012, background): “In theoretical aspects, uncertain process [8], uncertain differential equation [9] and uncertain set theory [10] have been established.”
• Uncertain programming model for uncertain optimal assignment problem (2013, background): “After that, Chen and Liu [6] proved the existence and uniqueness theorem for uncertain differential equations.”
• A New Option Pricing Model for Stocks in Uncertainty Markets (2011, background): “By the European put option pricing formula (3), we effectively calculate out that the price is0.”
• Asian Option Pricing Formula for Uncertain Financial Market (2015, methodology): “Chen and Liu [3] proved the existence and uniqueness theorem for uncertain differential equations.”
• Runge-Kutta Method for Solving Uncertain Differential Equations (2015, methodology): “Chen and Liu [11] figured out the analytic solution of the linear uncertain differential equation.”
• OPTIMISTIC VALUE MODEL OF UNCERTAIN OPTIMAL CONTROL (2013, unknown): “So we have M{aξ + bξ2 ≥ y} ≤ M{aξ + bd2 ≥ y}+ ε. Letting M{aξ + bξ2 ≥ y} ≥ α, we have M{aξ + bd2 ≥ y}+ ε ≥ α, or M{aξ + bd2 ≥ y} ≥ α− ε. (22) It follows from Inequality (22) and the definition of optimistic value that y ≤ (aξ + bd2)sup(α− ε) = (aξ)sup(α− ε) + bd2.”
• Extreme values and integral of solution of uncertain differential equation (2013, background): “Chen and Liu [14] gave an analytic solution for linear uncertain differential equation.”
• Uncertain Programming Model for Chinese Postman Problem with Uncertain Weights (2012, background): “After that, Chen and Liu (2010) proved the existence and uniqueness theorem for uncertain differential equations.”
• Maximum Entropy Principle for Uncertain Variables (2011, background): “The expected value operator of uncertain variable was defined by Liu [13] as 0 0 d [ d ] { } { } E r r r M r M ξ ξ ξ +∞ −∞ = ≥ − ≤ ∫ ∫ provided that at least one of the two integrals is finite.”
• Uncertain Risk Analysis and Uncertain Reliability Analysis (2010, methodology): “After that, an existence and uniqueness theorem of solution of uncertain differential equation was proved by Chen and Liu [2] in 2010.”
• Existence and uniqueness of the solution to uncertain fractional differential equation (2015, background): “An existence and uniqueness theorem of solution for the uncertain differential equation (1) was proved by Chen and Liu [21].”
• Toward uncertain finance theory (2013, methodology): “For example, Chen and Liu [5] showed that the linear uncertain differential equation dXt = (u1tXt + u2t)dt + (v1tXt + v2t)dCt (37)”
• Liu process and uncertain calculus (2013, background): “After that, Chen and Liu [16] proved the existence and uniqueness theorem for uncertain differential equations.”
• Uncertain differential games with application to capitalism (2013, background): “(Chen and Liu [19]) The uncertain differential equation”