| Liu process is a kind of fuzzy process,it can be used to describe the dynamic fuzzy phenomenon,it has stationary and independent increments,furthermore the increment is still a fuzzy variable.The aim of this paper is to study fuzzy differential equation driven by Liu process.Nowadays,researches on fuzzy differential equations can be generally divided into two categories.One is the fuzzy differential equations which are obtained by fuzzing the coefficients of classical differential equations or fuzzing the initial conditions of classical differential equations.Another is fuzzy differential equations driven by Liu process.Compared to the former,the latter is driven by a fuzzy process,so the fuzziness of fuzzy differential equation is not only reflected in the initial conditions and coefficients,but also reflected in the driving process.In other words,fuzzy differential equation driven by Liu process has more extensive applications.In the framework of credibility theory,this paper will discuss the stability of fuzzy differential equations driven by Liu process and numerical methods for fuzzy differential equations driven by Liu process based on Liu integral and Liu differential.The main contents are as follows:1.The concepts of stability in credibility and stability in mean for fuzzy differential equation driven by Liu process are proposed in this paper,then some corresponding sufficient conditions of stability in credibility and stability in mean are derived.What is more,the conclusions are extended to the case of multi-dimensional.2.Fuzzy Taylor expansion is derived in this paper.Two numerical methods for fuzzy differential equation driven by Liu process are obtained based on fuzzy Taylor expansion.They are fuzzy Euler method and a numerical method based on fuzzy Taylor expansion.Then the local convergence of these two kinds of numerical methods are proven.In addition,the multidimensional fuzzy Euler method is obtained and the corresponding local convergence is proved. |
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