Moscow Mathematical Journal

Volume 19, Issue 1, January–March 2019 pp. 89–106.

On Convergence of 1D Markov Diffusions to Heavy-Tailed Invariant Density

Authors: O.A. Manita (1), A.Yu. Veretennikov(2)
Author institution:(1) Moscow State University, Moscow, Russia
(2) University of Leeds, UK, & National Research University Higher School of Economics, & Institute for Information Transmission Problems, Moscow, Russia

Summary:

Rate of convergence is studied for a diffusion process on the half line with a non-sticky reflection to a heavy-tailed 1D invariant distribution whose density on the half line has a polynomial decay at infinity. Starting from a standard recipe, which guarantees some polynomial convergence, it is shown how to construct a new non-degenerate diffusion process on the half line which converges to the same invariant measure exponentially fast uniformly with respect to the initial data.

2010 Math. Subj. Class. 60H10, 60J60.

Keywords: 1D diffusion, invariant distribution, heavy tails, fast convergence.

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