Driven by a Liu process, backward uncertain differential equation is a type of differential equations with given final value. So far, the concepts of stability in measure, stability in mean and stability in pth moment for backward uncertain differential equations have been proposed. As a supplement, this paper is concerned with two other kinds of stability of backward uncertain differential equations, and proposes the concepts of almost sure stability and pth moment exponential stability. In addition, some sufficient conditions for backward uncertain differential equations being stable almost surely or pth moment exponentially are derived.
AllahviranlooT., KianiN.A. and BarkhordariM., Toward the existence and uniqueness of solutions of second-order fuzzy differential equations, Information Sciences179(8) (2009), 1207–1215.
2.
ChenX. and LiuB., Existence and uniqueness theorem for uncertain differential equations, Fuzzy Optimization and Decision Making9(1) (2010), 69–81.
3.
ChenX. and GaoJ., Uncertain term structure model of interest rate, Soft Computing17(4) (2013), 597–604.
4.
DiamondP., Stability and periodicity in fuzzy differential equations, IEEE Transactions on Fuzzy Systems8(5) (2000), 583–590.
5.
GaoR., Milne method for solving uncertain differential equations, Applied Mathematics and Computation274 (2016), 774–785.
6.
GeX. and ZhuY., A necessary condition of optimality for uncertain optimal control problem, Fuzzy Optimization and Decision Making12(1) (2013), 41–51.
7.
HoaN.V., TriP.V., DaoT.T. and ZelinkaI., Some global existence results and stability theorem for fuzzy functional differential equations, Journal of Intelligent and Fuzzy Systems28 (2015), 393–409.
LiuB., Fuzzy process, hybrid process and uncertain process, Journal of Uncertain Systems2(1) (2008), 3–16.
10.
LiuB., Some research problems in uncertainty theory, Journal of Uncertain Systems1 (2009), 3–10.
11.
ShenY. and YaoK., A mean-reverting currency model in an uncertain environment, Soft Computing20(10) (2016), 4131–4138.
12.
WangX., NingY., MoughalT. and ChenX., Adams-Simpson method for solving uncertain differential equation, Applied Mathematics and Computation271 (2015), 209–219.
13.
WangX. and NingY., Stability of uncertain delay differential equations, Journal of Intelligent and Fuzzy Systems32(3) (2017), 2655–2664.
14.
WangX. and NingY., An uncertain currency model with floating interest rates, Soft Computingdoi: 10.1007/s00500-016-2224-9.
15.
WangX. and NingY., Stability analysis of backward uncertain differential equations, under review.
16.
YangX. and GaoJ., Linear-quadratic uncertain differential game with application to resource extraction problem, IEEE Transactions on Fuzzy Systems24(4) (2016), 819–826.
17.
YangX. and YaoK., Uncertain partial differential equation with application to heat vonduction, Fuzzy Optimization and Decision Making. doi: 10.1007/s10700-016-9253-9.
18.
YaoK., GaoJ. and GaoY., Some stability theorems of uncertain differential equation, Fuzzy Optimization and Decision Making12(1) (2013), 3–13.
19.
YaoK., Uncertain differential equation with jumps, Soft Computing19(7) (2015), 2063–2069.
20.
YuX., A stock model with jumps for uncertain markets, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems20(3) (2012), 421–432.
21.
ZhuY., Uncertain optimal control with application to a portfolio selection model, Cybernetics and Systems41(7) (2010), 535–547.
