Open Access
June 2014 Asymptotic equivalence of nonparametric diffusion and Euler scheme experiments
Valentine Genon-Catalot, Catherine Larédo
Ann. Statist. 42(3): 1145-1165 (June 2014). DOI: 10.1214/14-AOS1216


We prove a global asymptotic equivalence of experiments in the sense of Le Cam’s theory. The experiments are a continuously observed diffusion with nonparametric drift and its Euler scheme. We focus on diffusions with nonconstant-known diffusion coefficient. The asymptotic equivalence is proved by constructing explicit equivalence mappings based on random time changes. The equivalence of the discretized observation of the diffusion and the corresponding Euler scheme experiment is then derived. The impact of these equivalence results is that it justifies the use of the Euler scheme instead of the discretized diffusion process for inference purposes.


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Valentine Genon-Catalot. Catherine Larédo. "Asymptotic equivalence of nonparametric diffusion and Euler scheme experiments." Ann. Statist. 42 (3) 1145 - 1165, June 2014.


Published: June 2014
First available in Project Euclid: 20 June 2014

zbMATH: 1246.62137
MathSciNet: MR3224284
Digital Object Identifier: 10.1214/14-AOS1216

Primary: 62B15 , 62G20
Secondary: 60J60 , 62M99

Keywords: deficiency distance , diffusion process , Discrete observations , Euler scheme , Le Cam equivalence , Nonparametric experiments

Rights: Copyright © 2014 Institute of Mathematical Statistics

Vol.42 • No. 3 • June 2014
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