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* Corresponding author 1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires 2 LaMME - Laboratoire de Mathématiques et Modélisation d-Evry

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. Unlike most of the classical maximum likelihood approach, the limit of the criterion function is in general a nondegenerate random variable and convergence does not hold in probability. Not only the leading term but also the second order asymptotics is needed to fully identify the unknown parameter. We present different frameworks to illustrate these facts. We also explore the numerical performance of our estimation procedure.

Keywords : Recurrent regime maximum likelihood estimation random walk in random environment





Autor: Francis Comets - Mikael Falconnet - Oleg Loukianov - Dasha Loukianova -

Fuente: https://hal.archives-ouvertes.fr/



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