| Let H be a Hilbert space and E a Banach space.In this paper,we set up a theory about the stochastic integration,which is about the integration of L(H,E)-valued functions,the functions is related to an H-cylindrical Liouville fractional Brownian motion,letβrepresent the Hurst parameter of an H-cylindrical Liouville fractional Brownian motion,whereβhas a value range of0<β<1.Further,for0<β<1/2 we show that a functionΦ:(0,T)→L(H,E)is stochastically integrable with respect to an H-cylindrical Liouville fractional Brownian motion if and only if it is stochastically integrable with respect to an H-cylindrical fractional Brownian motion.Then,we study a class of stochastic evolution equations driven by H-cylindrical Liouville fractional Brownian motion,that is dU(t)=AU(t)dt+BdW_H~β(t) and we can prove the existence,uniqueness and space-time regularity of mild solutions on the Banach space E under the assumption ofβwith different values,in which has operators A:?(A)→E and B:H→E,the Hurst parameter isβ.Finally,the above results are applied to a class of second-order parabolic stochastic partial differential equations driven by space-time noise,and it is proved that there exists a mild solution for the problem when d/4<β<1. |
