Long‐Time Behaviour of Langevin Algorithms with Time‐dependent Energy Function

Abstract

We study the Langevin algorithm on C" n-dimensional compact connected Riemannian manifolds and on R", allowing the energy function U to vary with time. We find conditions under which the distribution of the process at hand becomes indistinguishable as t + co from the "instantaneous" equilibrium distribution. Such conditions do not necessarily imply that U ( t ) converges pointwise as t + 00.