Stability Of Stochastic Differential Equations Driven By G-Lévy Process With Feedback Control

This dissertation mainly considers the stability of three kinds of stochastic differential equations driven by G-Levy process with feedback control.The full text is divided into four parts.In the first part,we introduce the background,current situations about the research and some necessary definitions and lemmas.In the second part,for the unstable stochastic differential equations driven by G-Levy process dx(t)=f(t,x(t))dt+h(t,x(t))d<B>(t)+?(t,x(t))dB(t)+?R0d K(t,x(t),z)L(dt,dz),we design a discrete time feedback control u(t,x([t/?]?))in the drift so that the controlled system becomes mean square exponentially stable by the Lyapunov function.At last,we give an example to verify the obtained theory.In the third part,we discuss the stochastic differential equations driven by G-Levy process dx(t)=f(t,x(t))dt+h(t,x(t))d<B>(t)+?(t,x(t))dB(t)+?R0d K(t,x(t),z)L(dt,dz),our aim is to design delay feedback control u(t,x(t-?))in the drift and obtain the asymptotical stability in mean square and quasi-surely asymptotical stability for the stochastic differential equations driven by G-Levy process with the polynomial growth condition.Then we give an example to verify the obtained theory.In the fourth part,for the unstable ordinary differential equations dx(t)=f(t,x(t))dt,we design stochastic perturbation h(t,x(t/?]?)),?(t,x([t/?]?)),K(t,x([t/?]?),z)to s.t.it bounded.Then we obtain the mean square exponential bounded and quasi-sure exponential bounded for the controlled systems.At last,we give an example to verify the obtained theory.