The weight-per-symbol polytope and scaffolds of invariants associated with Markov chains
The weight-per-symbol polytope and scaffolds of invariants associated with Markov chains
复制标题
与马尔可夫链相关的每个符号的重量多面体和不变量的支架
DOI：
--
复制
发表时间：
1991
影响因子：
0.9
通讯作者：
Selim Tuncel
中科院分区：
文献类型：
--
作者：
B. Marcus;Selim Tuncel
摘要利用周期轨道构造的不变量研究马尔可夫链。在这些不变量的基础上，正则扩展被用来建立一个有限到一的块同态从一个马尔可夫链到另一个马尔可夫链的程度的约束。我们利用周期轨道的归一化权构造了一个多面体。利用这一多面体，我们在原始马尔可夫链中找到了标准定义的诱导马尔可夫链。每一个与这些马尔可夫链相关的不变量都会产生一个原始马尔可夫链的不变量支架。利用这一方法得到了有限等价猜想和有限期望编码时间有限同构猜想的反例。还包括与马尔可夫链类中的伯努利位移的极小性问题相关的结果（关于块同态），其函数等于伯努利位移的函数。
Abstract We study Markov chains via invariants constructed from periodic orbits. Canonical extensions, based on these invariants, are used to establish a constraint on the degree of finite-to-one block homomorphisms from one Markov chain to another. We construct a polytope from the normalized weights of periodic orbits. Using this polytope, we find canonically-defined induced Markov chains inside the original Markov chain. Each of the invariants associated with these Markov chains gives rise to a scaffold of invariants for the original Markov chain. This is used to obtain counterexamples to the finite equivalence conjecture and to a conjecture regarding finitary isomorphism with finite expected coding time. Also included are results related to the problem of minimality (with respect to block homomorphism) of Bernoulli shifts in the class of Markov chains with beta function equal to the beta function of the Bernoulli shift.