所有α混合过程的命中和返回到罕见事件
Hitting and returning into rare events for all alpha-mixing processes
摘要：
证明了对任意$α$混合平稳过程，任意$n$串$A_n$的首中时在适当的归一化条件下收敛于一个指数律.我们确定了归一化常数$λ(A_n)$。类似的陈述也适用于返回时间。为了建立这个结果，我们证明了两个独立的利益的其他结果。首先，我们证明了重标首中时和重标返回时之间的关系，推广了Haydn，Lacroix和Vaienti的一个定理。其次，我们证明了对于正熵系统，当$n$趋于无穷大时，在$n$连续观测中观测到任何$n$ -弦的概率趋于零。
英文摘要：
We prove that for any $α$-mixing stationnary process the hitting time of any $n$-string $A_n$ converges, when suitably normalized, to an exponential law. We identify the normalization constant $λ(A_n)$. A similar statement holds also for the return time. To establish this result we prove two other results of independent interest. First, we show a relation between the rescaled hitting time and the rescaled return time, generalizing a theorem by Haydn, Lacroix and Vaienti. Second, we show that for positive entropy systems, the probability of observing any $n$-string in $n$ consecutive observations, goes to zero as $n$ goes to infinity.
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