  We introduce a new diffusion process which arises as the $n\to\infty$ limit
of a Bessel process of dimension $d \ge 2$ conditioned upon remaining bounded
below one until time $n$. In addition to being interesting in its own right, we
argue that the resulting diffusion process is a natural hard edge counterpart
to the Ferrari-Spohn diffusion of arXiv:math/0308242. In particular, we show
that the generator of our new diffusion has the same relation to the
Sturm-Liouville problem for the Bessel operator that the Ferrari-Spohn
diffusion does to the corresponding problem for the Airy operator.
