@article{Kangkang_2011, title={A class of strong limit theorems for nonhomogeneous Markov chains indexed by a generalized Bethe tree on a generalized random selection system}, volume={63}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/2810}, abstractNote={We study strong limit theorems for a bivariate function sequence of an nonhomogeneous Markov chain indexed
by a generalized Bethe tree on a generalized random selection system by constructing a nonnegative martingale.
As corollaries, we generalize results of Yang and Ye and obtain some limit theorems for frequencies of states,
ordered couples of states, and the conditional expectation of a bivariate function on Cayley tree.}, number={10}, journal={Ukrainsâ€™kyi Matematychnyi Zhurnal}, author={Kangkang, Wang}, year={2011}, month={Oct.}, pages={1336-1351} }