In this paper, we establish a new limit theorem for partial sums of random variables. As corollaries, we generalize the extended Borel-Cantelli lemma, and obtain some strong laws of large numbers for Markov chains as well as a generalized strong ergodic theorem for irreducible and positive...

In this paper, we use an analytic approach to study the limit properties of {inn(Xn)}, the functional of a countable nonhomogeneous Markov chain {Xn}. A class of strong laws of large numbers for these processes, which are different from the usual ones, are obtained. In the theorems of this...

In this paper, we study the strong law of large numbers on the frequencies of states for a Markov chains field on a Bethe tree. In the proof, we apply a new technique in the study of the strong limit theorem.

Combining the disputes on the “normal development†and “natural growth existing in farmers†cooperatives and according to the actual investigation statistics, the management model selection and regulation (including model selection, policy encouragement, operation scale and...

This paper presents the ability of the existing Chinese energy system to integrate wind power and explores how the Chinese energy system needs to prepare itself in order to integrate more fluctuating renewable energy in the future. With this purpose in mind, a model of the Chinese energy system...

“Concentrate-and-degrade” is an effective strategy to promote mass transfer and degradation of pollutants in photocatalytic systems, yet suitable and cost-effective photocatalysts are required to practice the new concept. In this study, we doped a post-transition metal of Indium (In) on a...