具有连续性条件的无界记忆Markov类的冗余性
Redundancy of unbounded memory Markov classes with continuity conditions
摘要：
本文研究了由二进制马尔可夫源$p$产生的串$X_1,\dots, X_n$在没有任何内存限制的情况下的通用压缩的冗余性。为了更好地理解压缩和估计之间的联系，在马尔可夫制度，我们考虑一类马尔可夫源的连续性条件的限制。在没有记忆上限的情况下，连续性条件意味着随着$m$的增加，$p(X_0|X^{-1}_{-m})$更接近真实概率$p(X_0|X_{-\infty}^{-1})$，而不是任意变化。对于这样的源，我们证明渐近匹配的上界和下界的冗余。在这个过程中，我们从冗余的角度确定类中的哪些源最重要。
英文摘要：
We study the redundancy of universally compressing strings $X_1,\dots, X_n$ generated by a binary Markov source $p$ without any bound on the memory. To better understand the connection between compression and estimation in the Markov regime, we consider a class of Markov sources restricted by a continuity condition. In the absence of an upper bound on memory, the continuity condition implies that $p(X_0|X^{-1}_{-m})$ gets closer to the true probability $p(X_0|X_{-\infty}^{-1})$ as $m$ increases, rather than vary around arbitrarily. For such sources, we prove asymptotically matching upper and lower bounds on the redundancy. In the process, we identify what sources in the class matter the most from a redundancy perspective.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
