Semilinear stochastic equations in a Hilbert space with a fractional Brownian motion

This is the published version, also available here: http://dx.doi.org/10.1137/08071764X.The solutions of a family of semilinear stochastic equations in a Hilbert space with a fractional Brownian motion are investigated. The nonlinear term in these equations has primarily only a growth condition assumption. An arbitrary member of the family of fractional Brownian motions can be used in these equations. Existence and uniqueness for both weak and mild solutions are obtained for some of these semilinear equations. The weak solutions are obtained by a measure transformation that verifies absolute continuity with respect to the measure for the solution of the associated linear equation. Some examples of stochastic differential and partial differential equations are given that satisfy the assumptions for the solutions of the semilinear equations

A Note on variational solutions to SPDE perturbed by Gaussian noise in a general class

This note deals with existence and uniqueness of (variational) solutions to the following type of stochastic partial differential equations on a Hilbert space H dX(t) = A(t,X(t))dt + B(t,X(t))dW(t) + h(t) dG(t) where A and B are random nonlinear operators satisfying monotonicity conditions and G is an infinite dimensional Gaussian process adapted to the same filtration as the cylindrical Wiener pocess W(t), t >= 0