  We look at the equilibrium of a Brownian particle in an inhomogeneous space
following the alternative approach proposed in ref.[1]. We consider a
coordinate dependent damping that makes the stochastic dynamics the one with
multiplicative noise. Here we show that the mapping to an additive noise gives
the equilibrium distribution of the generalized Langevin dynamics of a particle
with mass. The procedure does not need inclusion of any ad hoc current
cancelling term in the Langevin dynamics. The result shows a modified
Maxwell-Boltzmann distribution with a damping dependent amplitude.
