  We introduce a pathwise integration for Volterra processes driven by L\'evy
noise or martingale noise. These processes are widely used in applications to
turbulence, signal processes, biology, and in environmental finance. Indeed
they constitute a very flexible class of models, which include fractional
Brownian and L\'evy motions and it is part of the so-called ambit fields. A
pathwise integration with respect of such Volterra processes aims at producing
a framework where modelling is easily understandable from an information
perspective. The techniques used are based on fractional calculus and in this
there is a bridging of the stochastic and deterministic techniques. The present
paper aims at setting the basis for a framework in which further computational
rules can be devised. Our results are general in the choice of driving noise.
Additionally we propose some further details in the relevant context
subordinated Wiener processes.
