  We consider a class of stochastic processes containing the classical and
well-studied class of Squared Bessel processes. Our model, however, allows the
dimension be a function of the time. We first give some classical results in a
larger context where a time-varying drift term can be added. Then in the
non-drifted case we extend many results already proven in the case of classical
Bessel processes to our context. Our deepest result is a decomposition of the
Bridge process associated to this generalized squared Bessel process, much
similar to the much celebrated result of J. Pitman and M. Yor. On a more
practical point of view, we give a methodology to compute the Laplace transform
of additive functionals of our process and the associated bridge. This permits
in particular to get directly access to the joint distribution of the value at
t of the process and its integral. We finally give some financial applications
to illustrate the panel of applications of our results.
