中文摘要：

提出了Markov链的转移过程张量,在一步转移概率矩阵的基础上考虑将多步转移概率信息存储至转移过程张量,研究了Markov链的转移过程张量的弱不可约性,给出了它与一步转移概率矩阵不可约性之间的关系.此外还定义了超随机张量,并初步研究了这一类张量与转移过程张量之间的关系.

英文摘要：

The concept of transition process tensor is proposed, and the information of multi-step transition probability for Markov chain is considered to be stored in a transition process tensor. The weak irreducibility of transition process tensor for Markov chain is studied, and the connection between the reducibility and irreducibility of transition probability matrix and transition process tensor are established. Besides, the relationship between this tensor and super-stochastic tensor is discussed.