Asymptotic equivalence of nonparametric diffusion and Euler scheme experiments
非参数扩散与欧拉离散格式统计实验的渐近等价性
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…