  We extend the new approach introduced in arXiv:1912.02064v2 [math.PR] and
arXiv:2102.10119v1 [math.PR] for dealing with stochastic Volterra equations
using the ideas of Rough Path theory and prove global existence and uniqueness
results. The main idea of this approach is simple: Instead of the iterated
integrals of a path comprising the data necessary to solve any equation driven
by that path, now iterated integral convolutions with the Volterra kernel
comprise said data. This leads to the corresponding abstract objects called
Volterra-type Rough Paths, as well as the notion of the convolution product, an
extension of the natural tensor product used in Rough Path Theory.
