In dynamical systems, understanding statistical properties shared by most orbits and how these properties depend on the system are basic and important questions. Statistical properties may persist as one perturbs the system (statistical stability is said to hold), or may vary wildly. The latter case is our subject of interest, and we ask at what timescale does statistical stability break down. This is the time needed to observe, with a certain probability, a substantial difference in the statistical properties as described by (large but finite time) Birkhoff averages.

The quadratic (or logistic) family is a natural and fundamental example where statistical stability does not hold. We study this family. When the base parameter is of Misiurewicz type, we show, sharply, that if the parameter changes by t, it is necessary and sufficient to observe the system for a time at least of the order of $|t{|}^{-1}$ to see the lack of statistical stability.

在动力学系统中，了解大多数轨道共享的统计属性以及这些属性如何依赖系统是基本且重要的问题。统计属性可能会随着系统的扰动而持续（据说统计稳定性会保持不变），或者可能会发生巨大变化。后一种情况是我们感兴趣的主题，我们问统计稳定性在什么时间尺度上崩溃。这是以一定的概率观察到统计属性上的巨大差异所需要的时间，如（大但有限的时间）伯克霍夫平均值所描述的。

二次（或逻辑）族是一个自然且基本的示例，其中统计稳定性不成立。我们研究这个家庭。当基本参数为Misiurewicz类型时，我们可以清楚地表明，如果参数改变t，则有必要且充分的时间观察该系统至少大约为$|Ť{|}^{-\mathrm{1个}}$ 看缺乏统计稳定性。