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Matematicheskie Zametki, 2009, Volume 86, Issue 6, Pages 903–911
DOI: https://doi.org/10.4213/mzm4614 (Mi mzm4614) 		 
The Limit of Measures Generated by Diffusions with Unboundedly Increasing Drift

P. Yu. Tarasenko

M. V. Lomonosov Moscow State University
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DOI: https://doi.org/10.4213/mzm4614
Abstract: 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.
Received: 20.02.2008
Revised: 20.01.2009
English version:
Mathematical Notes, 2009, Volume 86, Issue 6, Pages 842–849
DOI: https://doi.org/10.1134/S0001434609110261
Bibliographic databases:
UDC: 519.218.1+519.216.7+517.987.1
Language: Russian
Citation: P. Yu. Tarasenko, “The Limit of Measures Generated by Diffusions with Unboundedly Increasing Drift”, Mat. Zametki, 86:6 (2009), 903–911; Math. Notes, 86:6 (2009), 842–849
Citation in format AMSBIB
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