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We prove a global asymptotic equivalence of experiments in the sense of LeCam's theory. The experiments are a continuously observed diffusion withnonparametric drift and its Euler scheme. We focus on diffusions withnonconstant-known diffusion coefficient. The asymptotic equivalence is provedby constructing explicit equivalence mappings based on random time changes. Theequivalence of the discretized observation of the diffusion and thecorresponding Euler scheme experiment is then derived. The impact of theseequivalence results is that it justifies the use of the Euler scheme instead ofthe discretized diffusion process for inference purposes.

Asymptotic equivalence of nonparametric diffusion and Euler scheme experiments