Long term convergence rate of Smoluchowski-Kramers approximation by Stein's method

Shiyu Liu, Wei Liu, Lihu Xu

We consider the following second-order stochastic differential equation on ${\mathbb{R}}^{2d}$: \begin{equation*} dX_t^m=Y_t^mdt, \quad mdY_t^m=b(X_t^m)dt+σ(X_t^m)dB_t-Y^m_tdt, \end{…