Rough Volterra equations 2: Convolutional generalized integrals

We define and solve Volterra equations driven by a non-differentiable signal, by means of a variant of the rough paths theory which allows us to handle generalized integrals weighted by an exponential coefficient. The results are applied to a standard rough path x=(x1,x2)∈C2γ(Rm)×C22γ(Rm,m), with γ>1/3γ>1/3, which includes the case of fractional Brownian motion with Hurst index H>1/3H>1/3.