On convergence of 1D Markov diffusions to heavy-tailed invariant density

O. A. Manita; A. Yu. Veretennikov

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arXiv · 1807.10351

On convergence of 1D Markov diffusions to heavy-tailed invariant density

O. A. Manita·A. Yu. Veretennikov

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Abstract

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 which density on the half line has a polynomial decay at infinity. Starting from a standard receipt 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.

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O. A. Manita, A. Yu. Veretennikov. 2018-07-26. On convergence of 1D Markov diffusions to heavy-tailed invariant density. https://arxiv.org/abs/1807.10351

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