  In this paper we compare the Boltzmann distribution with a modified Boltzmann
distribution, that results from an It\^o-process considering thermal
equilibrium of a Brownian particle with coordinate dependent diffusion, in the
light of an existing experiment. The experiment was reported in 1994 by
Faucheux and Libchaber. The experiment made use of direct tracking of diffusion
of Brownian particles near a wall. Results of this experiment allows us to
compare the Boltzmann and the modified Boltzmann distribution without making
use of any adjustable parameter. A comparison of these two distributions with
the experimental results lends support to the consideration of thermodynamic
equilibrium of a Brownian particle with coordinate-dependent diffusion to be an
It\^o-process.
