Abstract：Some strong limit theorems relative to the geometric average of random transition probability for second-order nonhomogeneous Markov chains indexed by a tree were studied. The definition of the second-order nonhomogeneous Markov chains was introduced to propose a lemma. According to the lemma, some strong limit theorems relative to the geometric average of random transition probability with inequality for second-order nonhomogeneous Markov chains indexed by a tree were established. Some strong limit theorems relative to occasional occurred frequency of states with inequality for second-order nonhomogeneous Markov chains indexed by a tree were deduced. As corollaries, some strong limit theorems for finite nonhomogeneous Markov chains indexed by a tree were achieved.
2012, Vol. 33 
