论文标题
您能预测未来的鲁棒性？
How robustly can you predict the future?
论文作者
论文摘要
Hardin和Taylor \ Cite {MR2384262}证明，在几乎每个时间点上，都可以正确预测现实的任何功能 - 甚至无处可连续的功能。他们在\ cite {MR3100500}中显示，甚至可以安排预测因子在简单的时间转移方面具有稳健性，并询问它们是否可以在其他更为复杂的时间扭曲方面相对于其他更复杂的时间变形。 Bajpai和Velleman \ cite {MR3552748}部分回答了这个问题，后者提供了上层和下边界（在$ \ text {homeo}^+（\ mathbb {r}）$的$ \ text {homeo}^+（\ mathbb {r}）$上的固定器上的预测器上的稳健性。我们改善了两个边界，其中一些最终减少了Hölder定理的后果（每个阿基米德群体都是Abelian）。
Hardin and Taylor \cite{MR2384262} proved that any function on the reals -- even a nowhere continuous one -- can be correctly predicted, based solely on its past behavior, at almost every point in time. They showed in \cite{MR3100500} that one could even arrange for the predictors to be robust with respect to simple time shifts, and asked whether they could be robust with respect to other, more complicated time distortions. This question was partially answered by Bajpai and Velleman \cite{MR3552748}, who provided upper and lower frontiers (in the subgroup lattice of $\text{Homeo}^+(\mathbb{R})$) on how robust a predictor can possibly be. We improve both frontiers, some of which reduce ultimately to consequences of Hölder's Theorem (that every Archimedean group is abelian).
