A limit theorem for partial sums of random variables and its applications

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 recurrent Markov chains. [Copyright &y& Elsevier]