  The Feller process is an one-dimensional diffusion process with linear drift
and state-dependent diffusion coefficient vanishing at the origin. The process
is positive definite and it is this property along with its linear character
that have made Feller process a convenient candidate for the modeling of a
number of phenomena ranging from single neuron firing to volatility of
financial assets. While general properties of the process are well known since
long, less known are properties related to level crossing such as the
first-passage and the escape problems. In this work we thoroughly address these
questions.
