Liu process and uncertain calculus
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Doléans-Dade C, Meyer P: Universté de strasbourg séminaire de probabilités. Lect. Notes Math 1970, 5: 143–173.
Kallenberg O: Foundations of Modern Probability. New York: Springer; 1997.
Liu B: Why is there a need for uncertainty theory? J. Uncertain Syst 2012,6(1):3–10.
Liu B: Uncertainty Theory. Berlin: Springer; 2007.
Liu B: Fuzzy process, hybrid process and uncertain process. J. Uncertain Syst 2008,2(1):3–16.
Zhang X, Ning Y, Meng G: Delayed renewal process with uncertain interarrival times. Fuzzy Optimization Decis. Mak 2013,12(1):79–87. 10.1007/s10700-012-9144-7
Chen X: Variation analysis of uncertain stationary independent increment processes. Eur. J. Oper. Res 2012,222(2):312–316. 10.1016/j.ejor.2012.05.010
Liu B: Some research problems in uncertainty theory. J. Uncertain Syst 2009,3(1):3–10.
Liu B, Yao K: Uncertain integral with respect to multiple canonical processes. J. Uncertain Syst 2012,6(4):250–255.
Yao K: Uncertain calculus with renewal process. Fuzzy Optimization Decis. Mak 2012,11(3):285–297. 10.1007/s10700-012-9132-y
Chen X: Uncertain calculus with respected to finite variation processes. Technical Report. 2013. http://orsc.edu.cn/online/110303.pdf
Chen X, Liu B: Existence and uniqueness theorem for uncertain differential equations. Fuzzy Optimization Decis. Mak 2010,9(1):69–81. 10.1007/s10700-010-9073-2
Yao K, Gao J, Gao Y: Some stability theorems of uncertain differential equation. Fuzzy Optimization Decis. Mak 2013,12(1):3–13. 10.1007/s10700-012-9139-4
Liu Y: An analytic method for solving uncertain differential equations. J. Uncertain Syst 2012,6(4):244–249.
Yao K: A type of nonlinear uncertain differential equations with analytic solution. 2013.
Yao K, Chen X: A numerical method for solving uncertain differential equations. J. Intell. Fuzzy Syst 2013. in press
Zhu Y: Uncertain optimal control with application to a portfolio selection model. Cybern. Syst 2010,41(7):535–547. 10.1080/01969722.2010.511552
Chen X: American option pricing formula for uncertain financial market. Int. J. Oper. Res 2011,8(2):32–37.
Peng J, Yao K: A new option pricing model for stocks in uncertainty markets. Int. J. Oper. Res 2010,7(4):213–224.
Liu B: Uncertainty Theory,. 2013. http//:orsc.edu.cn/liu/ut.pdf
Liu B: Uncertainty Theory: A Branch of, Mathematics for Modeling Human Uncertainty. Berlin: Springer; 2010.
Liu Y, Ha M: Expected value of function of uncertain variables. J. Uncertain Syst 2010,4(3):181–186.