LONG-TIME BEHAVIOR OF LANGEVIN ALGORITHMS WITH TIME-DEPENDENT ENERGY FUNCTION

We study the Langevin algorithm on C(infinity) n-dimensional compact c onnected Riemannian manifolds and on R(n), allowing the energy functio n U to vary with time. We find conditions under which the distribution of the process at hand becomes indistinguishable, as t --> infinity f rom the ''instantaneous'' equilibrium distribution. Such conditions do not necessarily imply that U (t) converges pointwise as t --> infinit y.