论文标题
马尔可夫链上的树木
Block Markov Chains on Trees
论文作者
论文摘要
我们介绍了由无限根树索引的马尔可夫链（BMC）。事实证明，BMCS定义了一类新的树指数的马尔可夫进程。我们阐明了与马尔可夫链（MCS）和马尔可夫随机场（MRFS）有关的BMC的结构。主要表明，每个根的BMC的概率度量确实是马尔可夫链（MCS），但它们在被考虑的树上形成了马尔可夫随机场（MRF）的严格子类。相反，表征了一类BMC的MC。此外，我们确定在一维情况下，BMC类与MCS相吻合。但是，一维晶格的轻微扰动使我们成为了不是MC的BMC的一个例子。
We introduce block Markov chains (BMCs) indexed by an infinite rooted tree. It turns out that BMCs define a new class of tree-indexed Markovian processes. We clarify the structure of BMCs in connection with Markov chains (MCs) and Markov random fields (MRFs). Mainly, show that probability measures which are BMCs for every root are indeed Markov chains (MCs) and yet they form a strict subclass of Markov random fields (MRFs) on the considered tree. Conversely, a class of MCs which are BMCs is characterized. Furthermore, we establish that in the one-dimensional case the class of BMCs coincides with MCs. However, a slight perturbation of the one-dimensional lattice leads to us to an example of BMCs which are not MCs appear.
