Limit Theorems for the First Hitting Times Process of a Diffusion and Statistical Applications
研究了当扩散过程方差趋近于零时，基于递增水平首次击中时间观测的漂移参数估计，证明了最小对比估计量的一致性和渐近正态性。
This paper is concerned with the estimation of an unknown parameter 0 in the drift function of a diffusion (X,) when only the first hitting times of increasing levels a, x < a < A, are observed. For diffusions having positive drift, we obtain limit theorems for the first hitting times process as the variance of the diffusion goes to 0. We apply them to obtain a contrast function based on this observation. The minimum contrast estimator of 0 is shown to be consistent, asymp- totically normal and asymptotically equivalent to the maximum likelihood estimator based on the complete observation of (X,) up to the first hitting time of A.