NONNEGATIVE CHAINABLE MATRICES AND KOLMOGOROV'S CONDITION

The paper proves that an indecomposable nonnegative matrix is chainable if and only if it satisfies Kolmogorov's condition, under which the Markov chain determined by a stochastic matrix obeys the multidimensional local limit theorem. Bibliography: 8 titles.
1. Introduction This paper continues the study of nonnegative chainable matrices initiated in [1]. Familiarity with [1] is desirable, but all the necessary definitions and facts are provided below. Additional [...]