| This paper mainly studies the existence and uniqueness of solutions,stability,instability and stabilization of the following stochastic differential equations driven by G-Brownian motion(GSDE):x(t)=x0+?0tf(s,x(s))ds+?0th(s,x(s))d(s)+?0tg(s,x(s))dB(s),where t?0,x(0)=x0?Rn is the initial value,B(·)is one-dimensional G-Brownian motion,(B)(·)is the quadratic variation process of the G-Brownian motion B(·),coefficients f,h,g:R+ŚRn?Rn.The first chapter introduces the research background,the structure of this paper and some basic symbols and spaces to be used later.The second chapter introduces the relevant knowledge of stochastic differential equations driven by G-Brownian motion and uniform asymptotic stability function,and lists some lemmas that need to be used in this paper to prepare for the following content.In Chapter 3,we prove the existence and uniqueness of the solutions of the above stochastic differential equations driven by G-Brownian motion under local Lipschitz conditions,on the basis of by introducing the explosion time ?? giving the existence of the solutions on the maximal existence interval,the existence and uniqueness of the global solutions is proved by using the stop time technique.Based on the existence and uniqueness theorem of solutions in Chapter 3,in Chapter 4,the exponentially p-stability of stochastic differential equations driven by G-Brownian motion are studied by using uniform asymptotic stability function,and a new exponentially p-stability theorem is obtained,which allows LV to be indefinite and weakens the constraint.Finally,the corresponding example are given to illustrate the theoretical results.Similarly,after strict proof,in Chapter 5,new exponentially p-instability criterion for stochastic differential equations driven by G-Brownian motion is given by using uniform asymptotic stability function,this criterion weakens the constraint of the original exponentially p-instability criterion.Finally,the corresponding example are given.In Chapter 6,based on the original stabilization conclusion,a new stabilization theorem for stochastic differential equations driven by G-Brownian motion is discussed by using uniform asymptotic stability function,the obtained results weaken the conditional constraint of the previous stabilization theorem,finally,examples are given to illustrate the result. |
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