Distribution of the mean reversion estimator in the Ornstein–Uhlenbeck process
推导了奥恩斯坦-乌伦贝克过程中均值回复参数最大似然估计量的精确分布，通过数值积分和联合特征函数解析计算，适用于不同设定，蒙特卡洛验证了精确方法的可靠性，而渐近分布可能产生误导。
We derive the exact distribution of the maximum likelihood estimator of the mean reversion parameter (κ) in the Ornstein–Uhlenbeck process using numerical integration through analytical evaluation of a joint characteristic function. Different scenarios are considered: known or unknown drift term, fixed or random start-up value, and zero or positive κ. Monte Carlo results demonstrate the remarkably reliable performance of our exact approach across all the scenarios. In comparison, misleading results may arise under the asymptotic distributions, including the advocated infill asymptotic distribution, which performs poorly in the tails when there is no intercept in the regression and the starting value of the process is nonzero.