Asymptotic equivalence of discretely observed diffusion processes and their Euler scheme: small variance case



This paper establishes the global asymptotic equivalence, in the sense of the Le Cam \(\Delta \)-distance, between scalar diffusion models with unknown drift function and small variance on the one side, and nonparametric autoregressive models on the other side. The time horizon \(T\) is kept fixed and both the cases of discrete and continuous observation of the path are treated. We allow non constant diffusion coefficient, bounded but possibly tending to zero. The asymptotic equivalences are established by constructing explicit equivalence mappings.


Nonparametric experiments Deficiency distance Asymptotic equivalence Diffusion processes Autoregression 

Mathematics Subject Classification

Primary 62B15 Secondary 62G20, 60G5 



I would like to thank Valentine Genon-Catalot for several interesting discussions, especially in suggesting to taking into account the relation between diffusion processes with small variance and deterministic limits. Also, I would like to give a special thank to Pierre Étoré, with whom a lot of hours were spent discussing different approaches to the proof of Lemma 4.10. More generally, I am very grateful for all the time he has invested in supervising this project.


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Laboratoire LJKUniversité Joseph FourierGrenoble Cedex 09France

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