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Lyapunov functions for random walks and strings in random environment. (English) Zbl 0938.60065

Summary: We study two typical examples of countable Markov chains in random environment using the Lyapunov functions method: random walk and random string in random environment. In each case we construct an explicit Lyapunov function. Investigating the behavior of this function, we get the classification for recurrence, transience, ergodicity. We obtain new results for random strings in random environment, though we simply review well-known results for random walks using our approach.

MSC:

60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
60G50 Sums of independent random variables; random walks
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