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The quenched law of the iterated logarithm for one-dimensional random walks in a random environment


  • Mao, Mingzhi
  • Liu, Ting
  • Foryś, Urszula


In this work, we discuss the rate of convergence of one-dimensional random walks in a random environment. Using the hitting time decomposition, we prove that the speed of escape of random walks satisfies the quenched law of the iterated logarithm in a standard way.

Suggested Citation

  • Mao, Mingzhi & Liu, Ting & Foryś, Urszula, 2013. "The quenched law of the iterated logarithm for one-dimensional random walks in a random environment," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 52-60.
  • Handle: RePEc:eee:stapro:v:83:y:2013:i:1:p:52-60 DOI: 10.1016/j.spl.2012.08.016

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    References listed on IDEAS

    1. Hwang, S.Y. & Basawa, I.V., 2011. "Asymptotic optimal inference for multivariate branching-Markov processes via martingale estimating functions and mixed normality," Journal of Multivariate Analysis, Elsevier, vol. 102(6), pages 1018-1031, July.
    2. Hwang, S.Y. & Kim, S. & Lee, S.D. & Basawa, I.V., 2007. "Generalized least squares estimation for explosive AR(1) processes with conditionally heteroscedastic errors," Statistics & Probability Letters, Elsevier, vol. 77(13), pages 1439-1448, July.
    3. S. Y. Hwang & I. V. Basawa, 2005. "Explosive Random-Coefficient AR(1) Processes and Related Asymptotics for Least-Squares Estimation," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(6), pages 807-824, November.
    4. Jeganathan, P., 1995. "Some Aspects of Asymptotic Theory with Applications to Time Series Models," Econometric Theory, Cambridge University Press, vol. 11(05), pages 818-887, October.
    5. Monsour, Michael J. & Mikulski, Piotr W., 1998. "On limiting distributions in explosive autoregressive processes," Statistics & Probability Letters, Elsevier, vol. 37(2), pages 141-147, February.
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