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

IF 0.6 4区 数学 Q3 MATHEMATICS
O. Manita, A. Veretennikov
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引用次数: 0

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.
关于一维马尔可夫扩散对重尾不变密度的收敛性
研究了半线上的扩散过程对重尾1D不变分布的非粘性反射的收敛速度,该分布的密度在无穷远处具有多项式衰减。从保证多项式收敛的标准接收出发,给出了如何在半线上构造一个新的非退化扩散过程,该过程相对于初始数据以指数一致的速度收敛到相同的不变测度。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
1.40
自引率
0.00%
发文量
16
审稿时长
>12 weeks
期刊介绍: The Moscow Mathematical Journal (MMJ) is an international quarterly published (paper and electronic) by the Independent University of Moscow and the department of mathematics of the Higher School of Economics, and distributed by the American Mathematical Society. MMJ presents highest quality research and research-expository papers in mathematics from all over the world. Its purpose is to bring together different branches of our science and to achieve the broadest possible outlook on mathematics, characteristic of the Moscow mathematical school in general and of the Independent University of Moscow in particular. An important specific trait of the journal is that it especially encourages research-expository papers, which must contain new important results and include detailed introductions, placing the achievements in the context of other studies and explaining the motivation behind the research. The aim is to make the articles — at least the formulation of the main results and their significance — understandable to a wide mathematical audience rather than to a narrow class of specialists.
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