A Sufficient Condition for Asymptotic Sufficiency of Incomplete Observations of a Diffusion Process
扩散过程不完全观测渐近充分性的一个充分条件
Consider an $m$-dimensional diffusion process $(X_t)$ with unknown drift and small known variance observed on a time interval $\lbrack 0, T\rbrack$. We derive here a general condition ensuring the asymptotic sufficiency, in the sense of Le Cam, of incomplete observations of $(X_t)_{0 \leq t \leq T}$ with respect to the complete observation of the diffusion as the variance goes to 0. We then construct estimators based on these partial observations which are consistent,…