Some strong limit theorems for nonhomogeneous Markov chains indexed by controlled trees

Abstract

Abstract In this paper, a kind of infinite, local finite tree T, named a controlled tree, is introduced. Some strong limit properties, such as the strong law of large numbers and the asymptotic equipartition property, for nonhomogeneous Markov chains indexed by T, are established. The outcomes are the generalizations of some well-known results.

Keywords

• nonhomogeneous Markov chain
• controlled tree
• strong law of large numbers
• AEP