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Maximum likelihood estimator consistency for recurrent random walk in a parametric random environment with finite support

Author

Listed:
  • Comets, Francis
  • Falconnet, Mikael
  • Loukianov, Oleg
  • Loukianova, Dasha

Abstract

We consider a one-dimensional recurrent random walk in random environment (RWRE) when the environment is i.i.d. with a parametric, finitely supported distribution. Based on a single observation of the path, we provide a maximum likelihood estimation procedure of the parameters of the environment.

Suggested Citation

  • Comets, Francis & Falconnet, Mikael & Loukianov, Oleg & Loukianova, Dasha, 2016. "Maximum likelihood estimator consistency for recurrent random walk in a parametric random environment with finite support," Stochastic Processes and their Applications, Elsevier, vol. 126(11), pages 3578-3604.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:11:p:3578-3604
    DOI: 10.1016/j.spa.2016.04.034
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    References listed on IDEAS

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    1. Comets, Francis & Falconnet, Mikael & Loukianov, Oleg & Loukianova, Dasha & Matias, Catherine, 2014. "Maximum likelihood estimator consistency for a ballistic random walk in a parametric random environment," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 268-288.
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    Cited by:

    1. Diel, Roland & Lerasle, Matthieu, 2018. "Non parametric estimation for random walks in random environment," Stochastic Processes and their Applications, Elsevier, vol. 128(1), pages 132-155.
    2. Andreoletti, Pierre & Diel, Roland, 2020. "The heavy range of randomly biased walks on trees," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 962-999.
    3. Rémillard, Bruno N. & Vaillancourt, Jean, 2019. "Detecting periodicity from the trajectory of a random walk in random environment," Statistics & Probability Letters, Elsevier, vol. 155(C), pages 1-1.

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    3. Diel, Roland & Lerasle, Matthieu, 2018. "Non parametric estimation for random walks in random environment," Stochastic Processes and their Applications, Elsevier, vol. 128(1), pages 132-155.
    4. Andreoletti, Pierre & Diel, Roland, 2020. "The heavy range of randomly biased walks on trees," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 962-999.

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