On almost sure convergence for double arrays of dependent random variables

Small deviation properties concerning arrays of non-homogeneous Markov information sources

“…However, most of the aforementioned results do not consider arrays of information sources, which play significant roles in information science. In recent works, [30] explored the conditions and SLLNs for almost certain convergence of double random variable arrays, and [31] established several kinds of convergences for row negatively correlated random variable arrays under certain conditions. More related studies can be found in their references.…”

“…Therefore, the limit behavior and the AEP, as well as the small deviation properties of the arrays of information sources, aroused our interest. This paper, in line with [3], [30], and [31], first introduces the logarithmic likelihood ratio as a measure between arbitrary generalized information sources and non-homogeneous Markov sources and then establishes a class of generalized information sources for small deviation theorems and strong limit theorems. The outcomes generalize some existing results.…”