Stochastic evolution equations driven by Liouville fractional Brownian motion

Let H be a Hilbert space and E a Banach space. We set up a theory of stochastic integration of a"'(H,E)-valued functions with respect to H-cylindrical Liouville fractional Brownian motion with arbitrary Hurst parameter 0 < beta < 1. For 0 < beta < A1/2 we show that a function I broken vertical bar: (0, T) -> a"'(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. We apply our results to stochastic evolution equations driven by an H-cylindrical Liouville fractional Brownian motion, and prove existence, uniqueness and space-time regularity of mild solutions under various assumptions on the Banach space E, the operators A: D(A) -> E and B: H -> E, and the Hurst parameter. As an application it is shown that second-order parabolic SPDEs on bounded domains in a"e (d) , driven by space-time noise which is white in space and Liouville fractional in time, admit a mild solution if A1/4d < beta < 1.