Some properties of linear stochastic distributed parameter systems with fractional Brownian motion

A fractional Brownian motion with Hurst parameter in the interval (½, 1) is used for the Gaussian noise process in a linear stochastic distributed system or a linear stochastic partial differential equation. These noise processes have properties that have been important for finite dimensional systems. The notion of a mild solution is given and some conditions are given for the existence, the uniqueness and the sample path continuity of the solutions. Limiting distributions are given. Stochastic models with boundary noise instead of distributed noise are also considered. Some examples of a stochastic heat equation and a stochastic wave equation are given that satisfy the conditions for the results