  Let $\Phi$ a locally convex space and $\Psi$ be a quasi-complete,
bornological, nuclear space (like spaces of smooth functions and distributions)
with dual spaces $\Phi'$ and $\Psi'$. In this work we introduce sufficient
conditions for time regularity properties of the $\Psi'$-valued stochastic
convolution $\int_{0}^{t} \int_{U} S(t-r)'R(r,u) M(dr,du)$, $t \in [0,T]$,
where $(S(t): t \geq 0)$ is a $C_{0}$-semigroup on $\Psi$, $R(r,\omega,u)$ is a
suitable operator form $\Phi'$ into $\Psi'$ and $M$ is a cylindrical-martingale
valued measure on $\Phi'$. Our result is latter applied to study time
regularity of solutions to $\Psi'$-valued stochastic evolutions equations.
