Volterra Equations with Fractional Stochastic Integrals

We assume that a probability space (Ω,η,P) is given, where Ω denotes the space C(R+, Rk) equipped with the topology of uniform convergence on compact sets, η the Borel σ-field of Ω, and P a probability measure on Ω. Let {Wt(ω) = ω(t), t ≥ 0} be a Wiener process. For any t ≥ 0, we define ηt = σ{ω(s); s < t}∨Z, where Z denotes the class of the elements in ηt which have zero P-measure. Pardoux and Protter discussed the existence and uniqueness of the solution of the stochastic integral equation of the form