一类加性噪声为零的自回归模型的截断
Cutoff for a class of auto-regressive models with vanishing additive noise
摘要：
我们分析了一族自回归马尔可夫链$(X^{(n)}_k)_{k\geq 0}$在$\mathbb R^d$上的收敛速度，其中在每一步中，一个随机选择的坐标被替换为其他坐标的噪声阻尼加权平均。该模型的兴趣来自于与de Finetti在分析部分可交换数据时引入的某种贝叶斯方案的连接。我们的主要结果表明，当$n$变大（对应于消失的噪声），截止现象发生。
英文摘要：
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.
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