Markov链中的转移过程张量与超随机张量

Transition Process Tensor and Super Stochastic Tensor in Markov Chain

研究了一类特殊张量及其简单性质.从Markov链的转移概率矩阵出发,考虑到多步转移概率矩阵中所存储的信息仅表示从状态i经n步到达状态j的总概率,而无法从中直接读出转移过程途经各状态i1,i2,…,im-1的概率,因此提出了可用张量来存储相应的信息,称之为转移过程张量.在此基础上提出了超随机张量的概念,并根据Chapman-Kolmogorov方程证明了某些转移过程张量即为超随机张量.此外,研究了超随机张量的一些简单性质.

A special kind of tensor and its simple nature were studied and proved.Since the information stored in n-step transition probability matrix only expresses the total probability from state i to jin exactly nsteps,and cannot give the probability of going fromi to j via the states of i1,i2,…,im-1,a concept of transition process tensor was proposed to store these probabilities.Moreover,it also gave the definition of super stochastic tensor,according to Chapman-Kolmogorov equations,it was proved that some transition process tensors were super stochastic tensors.Some properties of super stochastic tensor were also studied.