Ergodicity of p-majorizing quadratic stochastic operators

Abstract

A scrambling square stochastic matrix plays an important role in the theory of the classical Markov chain. One of the classical results states that a row-stochastic matrix is strongly ergodic if and only if its some power is a scrambling matrix. In this paper, we deal with the similar problem for a cubic stochastic matrix. We introduce a notion of p-majorizing quadratic stochastic operators and study the strong ergodicity of p-majorizing quadratic stochastic operators associated with scrambling, Sarymsakov, and Wolfowitz cubic stochastic matrices. © 2018 Polymat Ltd. All rights reserved.

Citations and references