Asymptotic behavior of the Langevin equation for a nonhomogeneous medium

The Langevin equation has gained renewed interest through its role in modeling turbulent, reacting flow, and turbulent dispersion. Such applications often require an understanding of its long term, asymptotic behavior. The asymptotic, Smoluchowsky, equation is derived by constructing a uniformly valid bound on the velocity variance. Extra drift terms arise in the asymptotic equation when the coefficients are not constant.