Brownian motion on a manifold as a limit of Brownian motions with drift

Let R-n be n-dimensional Euclidean space and let M subset of R-n be a smooth compact m-dimensional Riemannian manifold ( without boundary) embedded in R-n. By a Brownian motion on M we mean a Markovian process whose transition semigroup is defined by the generator -1/2 Delta M, where Delta(M) stands for the Laplace-Beltrami operator on M (see, e. g., [2]). This note extends a series of papers in which a measure generated by a Brownian motion on M on the space of trajectories (with values in M) can be represented as the weak limit of measures on the space of trajectories in the ambient space R-n (see [7-10]). Namely, we claim that a sequence of diffusion processes on R-n which are Brownian motions with drift (in the direction of the manifold) with infinitely increasing modulus converges in distribution to a Brownian motion on the manifold.