Existence and uniqueness theorem for uncertain differential equations. (English) Zbl 1196.34005

Summary: Canonical process is a Lipschitz continuous uncertain process with stationary and independent increments, and uncertain differential equation is a type of differential equations driven by canonical process. This paper presents some methods to solve linear uncertain differential equations, and proves an existence and uniqueness theorem of solution for uncertain differential equation under Lipschitz condition and linear growth condition.


34A07 Fuzzy ordinary differential equations
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[1] Chen, X., & Ralescu, D. (2009). A note on truth value in uncertain logic. http://orsc.edu.cn/online/090211.pdf .
[2] Gao X. (2009) Some properties of continuous uncertain measure. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 17(3): 419–426 · Zbl 1180.28011
[3] Gao, X., & Ralescu, D. (2009). On Liu’s inference rule for uncertain systems. http://orsc.edu.cn/online/090121.pdf . · Zbl 1207.68386
[4] Li X., Liu B. (2009) Hybrid logic and uncertain logic. Journal of Uncertain Systems 3(2): 83–94
[5] Liu B. (2007) Uncertainty theory (2nd ed.). Springer, Berlin · Zbl 1141.28001
[6] Liu B. (2008) Fuzzy process, hybrid process and uncertain process. Journal of Uncertain Systems 2(1): 3–16
[7] Liu B. (2009a) Some research problems in uncertainty theory. Journal of Uncertain Systems 3(1): 3–10
[8] Liu B. (2009b) Theory and practice of uncertain programming (2nd ed.). Springer, Berlin · Zbl 1158.90010
[9] Liu, B. (2009c). Uncertainty theory (3rd ed.). http://orsc.edu.cn/liu/ut.pdf .
[10] Liu B. (2009d) Uncertain entailment and modus ponens in the framework of uncertain logic. Journal of Uncertain Systems 3(4): 243–251
[11] Peng, J. (2009). A stock model for uncertain markets. http://orsc.edu.cn/online/090209.pdf .
[12] Peng, Z., & Iwamura, K. (2009). A sufficient and necessary condition of uncertainty distribution. http://orsc.edu.cn/online/090305.pdf . · Zbl 1229.28029
[13] Qin, Z., & Kar, S. (2009). Single-period inventory problem under uncertain environment. http://orsc.edu.cn/online/090310.pdf . · Zbl 1290.90007
[14] Qin, Z., Kar, S., & Li, X. (2009). Developments of mean-variance model for portfolio selection in uncertain environment. http://orsc.edu.cn/online/090511.pdf .
[15] You C. (2009) Some convergence theorems of uncertain sequences. Mathematical and Computer Modelling 49(3–4): 482–487 · Zbl 1165.28310
[16] Zhu, Y. (2009). Uncertain optimal control with application to a portfolio selection model. http://orsc.edu.cn/online/090524.pdf .
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