Abstract.
We give a simplified proof, using elementary methods only, of the almost-sure central limit theorem (CLT) in any dimension for a Markov model of a random walk in a random environment introduced in [BMP].
References
Billingsley, P.: Convergence of Probability Measures, John Wiley & Sons, 1968
Bernabei, M.S., Boldrighini, C., Minlos, R.A., Pellegrinotti, A.: Almost-sure central limit theorem for a model of random walk in fluctuating random environment. Markov Processes Relat. Fields 4, 381–393 (1998)
Boldrighini, C., Minlos, R.A., Pellegrinotti, A.: Almost-sure central limit theorem for a Markov model of random walk in dynamical random environment. Probab. Relat. Fields 109, 245–273 (1997)
Gihman, I.I., Skorohod, A.V.: The theory of stochastic processes I, Springer, 1974
Author information
Authors and Affiliations
Corresponding author
Additional information
Mathematics Subject Classification (2000): 60F05, 60K37
Revised version: 29 January 2004
Rights and permissions
About this article
Cite this article
Stannat, W. A remark on the CLT for a random walk in a random environment. Probab. Theory Relat. Fields 130, 377–387 (2004). https://doi.org/10.1007/s00440-004-0359-6
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00440-004-0359-6
Keywords
- Random Walk
- Markov Model
- Limit Theorem
- Central Limit
- Central Limit Theorem