  Characterization of composite materials, whose properties vary in space over
microscopic scales, has become a problem of broad interdisciplinary interest.
In particular, estimation of the inhomogeneous transport coefficients, e.g. the
diffusion coefficient or the heat conductivity which shape important processes
in biology and engineering, is a challenging task. The analysis of such systems
is further complicated, because two alternative formulations of the
inhomogeneous transport equations exist in the literature -- the Smoluchowski
and Fokker-Planck equations, which are also related to the so-called
Ito-Stratonovich dilemma. Using the theory of statistical physics, we show that
the two formulations, usually regarded as distinct models, are physically
equivalent. From this result we develop efficient estimates for the transverse
space-dependent diffusion coefficient in fluids near a phase boundary. Our
method requires only measurements of escape probabilities and mean exit times
of molecules leaving a narrow spatial region. We test our estimates in three
case studies: (i) a Langevin model of a Buettikker-Landauer ratchet; atomistic
molecular-dynamics simulations of liquid-water molecules in contact with (ii)
vapor and (iii) soap (surfactant) film which has promising applications in
physical chemistry. Our analysis reveals that near the surfactant monolayer the
mobility of water molecules is slowed down almost twice with respect to the
bulk liquid. Moreover, the diffusion coefficient of water correlates with the
transition from hydrophilic to hydrophobic parts of the film.
