  This paper provides a Feller's test for explosions of one-dimensional
continuous stochastic Volterra processes of convolution type. The study focuses
on dynamics governed by nonsingular kernels, which preserve the semimartingale
property of the processes and introduce memory features through a
path-dependent drift. In contrast to the classical path-independent case, the
sufficient condition derived in this study for a Volterra process to remain in
the interior of an interval is generally more restrictive than the necessary
condition. The results are illustrated with three specifications of the
dynamics: the Volterra square-root diffusion, the Volterra Jacobi process and
the Volterra power-type diffusion. For the Volterra square-root diffusion, also
known as the Volterra CIR process, the paper presents a detailed discussion on
the approximation of the singular fractional kernel with a sum of exponentials,
a method commonly employed in the mathematical finance literature.
