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.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1216 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
