Ramification of Volterra-type rough paths

We extend the new approach introduced in [24] and [25] for dealing with stochastic Volterra equations using ideas of Rough Path theory prove global existence uniqueness results. The main idea this is simple: Instead iterated integrals a path comprising data necessary to solve any equation driven by that path, now integral convolutions kernel comprise said data. This leads corresponding abstract objects called Volterra-type Paths, as well notion convolution product, an extension natural tensor product used Theory.