论文标题
一类带有消失噪声的自动回归型号的截止
Cutoff for a class of auto-regressive models with vanishing additive noise
论文作者
论文摘要
我们分析了一个自动回归马尔可夫链$（x^{（n）} _ k）_ {k \ geq 0} $上的融合率，在$ \ mathbb r^d $上，在每个步骤中，随机选择的坐标被其他噪声的噪声均匀的坐标代替了其他噪声。该模型的兴趣来自De Finetti在分析部分可交换数据时引入的特定贝叶斯方案的联系。我们的主要结果表明，当$ n $变大（对应于消失的噪声）时，会发生截止现象。
We analyze the convergence rates for a family of auto-regressive Markov chains $(X^{(n)}_k)_{k\geq 0}$ on $\mathbb R^d$, where at each step a randomly chosen coordinate is replaced by a noisy damped weighted average of the others. The interest in the model comes from the connection with a certain Bayesian scheme introduced by de Finetti in the analysis of partially exchangeable data. Our main result shows that, when $n$ gets large (corresponding to a vanishing noise), a cutoff phenomenon occurs.
