Stability of the stochastic differential equation driven by fractional Brownian motion
The mean square exponential stability of the stochastic differential equations driven by fractional Brownian motion of the following form is considered,{dX(t)=(AX(t)+f(t,X(t))dt+g(t)dBH(t)X(t)=φ(t),t ∈[O,T]where H ∈(0,1/2).The moment estimation inequality is obtained by estimating the Wiener integral of the fractional Brownian motion in this equation.The stability of the mild solution is discussed by utilizing the integral inequality under some specific conditions.Corresponding examples are given to verify the accuracy of the conclusions.
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