Geodesic
The Limit of Measures Generated by Diffusions with Unboundedly Increasing Drift
Matematičeskie zametki, Tome 86 (2009) no. 6, pp. 903-911

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We prove that a sequence of diffusion processes in $\mathbb R^n$ that are Brownian motions with drift unboundedly increasing in modulus and directed to a manifold converges in distribution to the Brownian motion on the manifold.
Keywords: Brownian motion, unboundedly increasing drift, Riemannian manifold, Lipschitz condition, Laplace–Beltrami operator, semimartingale, Itô differential. 
@article{MZM_2009_86_6_a8,
     author = {P. Yu. Tarasenko},
     title = {The {Limit} of {Measures} {Generated} by {Diffusions} with {Unboundedly} {Increasing} {Drift}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {903--911},
     publisher = {mathdoc},
     volume = {86},
     number = {6},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2009_86_6_a8/}
}
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P. Yu. Tarasenko. The Limit of Measures Generated by Diffusions with Unboundedly Increasing Drift. Matematičeskie zametki, Tome 86 (2009) no. 6, pp. 903-911. http://geodesic.mathdoc.fr/item/MZM_2009_86_6_a8/