New Uniqueness Conditions for the Stationary Probability Matrix of Transition Probability Tensors

Several new uniqueness conditions for the stationary probability matrix of transition probability tensors arising from the higher-order multivariate Markov chains are given. Numerical examples are given to demonstrate that the new results are simpler and easier to be verified than the one provided by Li et al. (Comput Math Appl 78:1008-1025, 2019). As an application, a new convergence theorem for the power method to calculate the stationary probability matrix is given. Meanwhile, several perturbation bounds of the stationary probability matrix are obtained.

Automated summary

This paper provides several new uniqueness conditions for the stationary probability matrix of transition probability tensors arising from higher-order multivariate Markov chains. Numerical examples demonstrate that the new results are simpler and easier to verify compared to those provided by Li et al. (Comput Math Appl 78:1008-1025, 2019). Additionally, a new convergence theorem for the power method to calculate the stationary probability matrix is presented, along with several perturbation bounds of the matrix.