Existence and uniqueness of solutions to stochastic functional differential equations(0<H<1/2)driven by fractional Brownian motion
The existence and uniqueness of solutions for stochastic functional differential equations driven by fractional Brownian motion:({dX(t)=(ΑX(t)+f(t,Xt ))dt+g(t)dBH(t),t∈[0,T],X(t)=ζ(t),t ∈[-r,0],r≥0)are discussed by using Picard iterative method,where Hurst index is 0<H<1/2.Firstly,by estimating the integral of the fractional Brownian motion of the equation,the moment inequality of the random integral is obtained.Secondly,the mild solution of this kind of equation is defined by using analytic semigroup.Finally,under the relevant assumptions,the iterative sequence is constructed by using the iterative method,and it is proved that the mild solution of this kind of equation exists and is unique.
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