Maximum likelihood estimator consistency for a ballistic random walk in a parametric random environment

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:124

Article

Comets, Francis¹  Falconnet, Mikael²  Loukianov, Oleg^3,4  Loukianova, Dasha⁴  Matias, Catherine² 

[1] Univ Paris Diderot, Lab Probabilites & Modeles Aleatoires, UMR CNRS 7599, Paris, France

[2] Univ dEvry Val dEssonne, Lab Stat & Genome, UMR CNRS 8071, USC INRA, Evry, France

[3] Univ Paris Est, IUT Fontainebleau, Dept Informat, Paris, France

[4] Univ dEvry Val dEssonne, Lab Anal & Probabilites, Evry, France

关键词: Ballistic regime;    Branching process in random environment;    Maximum likelihood estimation;    Random walk in random environment;   

DOI  :  10.1016/j.spa.2013.08.002

来源: Elsevier

【 摘 要 】

We consider a one dimensional ballistic random walk evolving in an i.i.d. parametric random environment. We provide a maximum likelihood estimation procedure of the parameters based on a single observation of the path till the time it reaches a distant site, and prove that the estimator is consistent as the distant site tends to infinity. Our main tool consists in using the link between random walks and branching processes in random environments and explicitly characterising the limiting distribution of the process that arises. We also explore the numerical performance of our estimation procedure. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free