Stability Of Solutions To Impulsive Stochastic Differential Equations Driven By G-brownian Motion

In this paper, we mainly study the stability of solutions to impulsive stochastic differential equations driven by G-Brownian motion (IGSDEs in short) with the following torm. where f,hij,σj∈MG2([0,T];Rn), X0∈Rn is the initial value with E|X0|2<∞, and (<Bi,Bj>t)t≥t0 is the quadratic variation process of the G-Brownian motion (Bt)t≥t0· The impulsive function Ik ∈ C(Rn;Rn)(k∈N), the impulsive moments tk(k=1,2,...) satisfy 0≤to<t1<t2<…> and tkâ†'∞ as kâ†'∞.This thesis includes two respects. On the one hand, we establish the p-th moment stability and p-th moment asymptotical stability of solution by means of G-Lyapunov function method for system (1). An example is presented to illustrate the effectiveness of the obtained results.On the other hand, we study the exponential stability of solutions to IGSDEs, some criteria on p-th moment exponential stability and quasi sure exponential stability of the solutions are established by means of G-Lyapunov function method for system (1). Furthermore, an application is provided to illustrate the theory.