进程判别的一个不可能结果
An impossibility result for process discrimination
摘要：
给出了两个二元观测序列$x_1,x_1,...$和$y_1,y_2,...$：在每个时刻$n\in\N$，我们给出$x_n$和$y_n$。假设序列是由两个B过程相互独立地生成的。我们感兴趣的问题是，序列是否代表两个不同过程或同一过程的典型实现。我们证明，这是不可能决定的，在这个意义上说，每一个歧视程序是必然的错误与不可忽略的频率时，从一些B-过程的序列。这与早期的积极的结果B-过程，特别是那些表明，有一致的$\bar d$距离估计这类过程。
英文摘要：
Two series of binary observations $x_1,x_1,...$ and $y_1,y_2,...$ are presented: at each time $n\in\N$ we are given $x_n$ and $y_n$. It is assumed that the sequences are generated independently of each other by two B-processes. We are interested in the question of whether the sequences represent a typical realization of two different processes or of the same one. We demonstrate that this is impossible to decide, in the sense that every discrimination procedure is bound to err with non-negligible frequency when presented with sequences from some B-processes. This contrasts earlier positive results on B-processes, in particular those showing that there are consistent $\bar d$-distance estimates for this class of processes.
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