Some Limit Properties of the Harmonic Mean of Transition Probabilities for Markov Chains in Markovian Environments Indexed by Cayley's Trees

الملخص EN

We prove some limit properties of the harmonic mean of a random transition probability for finite Markov chains indexed by a homogeneous tree in a nonhomogeneous Markovian environment with finite state space.

In particular, we extend the method to study the tree-indexed processes in deterministic environments to the case of random enviroments.