Brownian motion on a manifold as a limit of Brownian motions with drift (Q1033754)

Let \(M\) be a smooth \(m\)-dimensional compact Riemannian manifold without boundary. Due to \textit{J. Nash}'s theorem [Ann. Math. (2) 63, 20--63 (1956; Zbl 0070.38603)] we can assume that it is isometrically embedded into a Euclidean space \(\mathbb{R}^n\). A Brownian motion on the manifold is the continuous Markov process whose transition semigroup is generated by \(-\frac{1}{2 }\Delta_M\) where \(\Delta_M\) is the Laplace-Beltrami operator on \(M\). In this note, the author proves that a sequence of Brownian motions with drift in the direction of the manifold \(M\) with infinitely increasing modulus converge in distribution to a Brownian motion on the manifold.