Hottovy, S.McDaniel, A.Wehr, J.Volpe, G.2015-07-282015-07-2820150010-3616http://hdl.handle.net/11693/12626We study a class of systems of stochastic differential equations describing diffusive phenomena. The Smoluchowski-Kramers approximation is used to describe their dynamics in the small mass limit. Our systems have arbitrary state-dependent friction and noise coefficients. We identify the limiting equation and, in particular, the additional drift term that appears in the limit is expressed in terms of the solution to a Lyapunov matrix equation. The proof uses a theory of convergence of stochastic integrals developed by Kurtz and Protter. The result is sufficiently general to include systems driven by both white and Ornstein-Uhlenbeck colored noises. We discuss applications of the main theorem to several physical phenomena, including the experimental study of Brownian motion in a diffusion gradient.EnglishBrownian ParticlesCharged-particleMagnetic-fieldDiffusionMotionThermophoresisApproximationPerturbationsIntegralsDynamicsArticle10.1007/s00220-014-2233-41432-0916