  In this work, we give a local non-determinism condition applicable to general
Volterra Ito processes that allow us to obtain the space-time regularity of the
occupation measure and the self-intersection measure. For the particular case
of solutions to a stochastic Volterra equation, we also obtain the regularity
of the one-dimensional distributions and study the absolute continuity of the
finite-dimensional distributions. Finally, based on the previously shown
regularity of the self-intersection measure, we prove the existence, uniqueness
and stability of Volterra equations with distributional drifts of
"self-intersection" type in terms of corresponding nonlinear Young equations.
