The Smoluchowski-Kramers approximation for n-dimensional generalized Langevin equation with state-dependent damping

We studied the Smoluchowski-Kramers approximation of a generalized Langevin equation with state-dependent damping in [Formula: see text]. Through a series of bounded estimates and tightness analysis, we obtain that the generalized Langevin equation converges in distribution to a limiting equation as the mass tends to 0.