Asymptotic equivalence of nonparametric diffusion and Euler scheme experiments
Valentine Genon-Catalot, Catherine Larédo
The Annals of Statistics · 2014 · Volume 42 · Issue 3
Abstract
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.
Keywords
60J60, 62B15, 62G20, 62M99, deficiency distance, diffusion process, Discrete observations, Euler scheme, Le Cam equivalence, Nonparametric experiments
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