  The Bessel process in low dimension (0 $\le$ $\delta$ $\le$ 1) is not an
It{\^o} process and it is a semimartingale only in the cases $\delta$ = 1 and
$\delta$ = 0. In this paper we first characterize it as the unique solution of
an SDE with distributional drift or more precisely its related martingale
problem. In a second part, we introduce a suitable notion of path-dependent
Bessel processes and we characterize them as solutions of path-dependent SDEs
with distributional drift.
