Open Access
October 1998 Lyapunov functions for random walks and strings in random environment
Francis Comets, Mikhail Menshikov, Serguei Popov
Ann. Probab. 26(4): 1433-1445 (October 1998). DOI: 10.1214/aop/1022855869


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.


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Francis Comets. Mikhail Menshikov. Serguei Popov. "Lyapunov functions for random walks and strings in random environment." Ann. Probab. 26 (4) 1433 - 1445, October 1998.


Published: October 1998
First available in Project Euclid: 31 May 2002

zbMATH: 0938.60065
MathSciNet: MR1675023
Digital Object Identifier: 10.1214/aop/1022855869

Primary: 60J10 , 60J80

Keywords: Disordered systems , Lyapunov exponents , Lyapunov function , Product of random matrices , random medium , random string , Random walk

Rights: Copyright © 1998 Institute of Mathematical Statistics

Vol.26 • No. 4 • October 1998
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