The Limit of Measures Generated by Diffusions with Unboundedly Increasing Drift

P. Yu. Tarasenko

M. V. Lomonosov Moscow State University

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.

UDC: 519.218.1+519.216.7+517.987.1

Received: 20.02.2008
Revised: 20.01.2009

DOI: 10.4213/mzm4614

 English version: Mathematical Notes, 2009, 86:6, 842–849

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