We study the disorder problem for a time-homogeneous diffusion process. The aim is to determine an efficient detection strategy of the disorder time $\theta$, at which the process changes its drift. We focus on the $\epsilon$-linear and the expected total miss criteria, where, unlike the well known linear penalty criterion, the expected penalty for an early/wrong detection of $\theta$ is expressed as the frequency of false alarms launched at least $\epsilon$ units of time before $\theta$ and as the expected advance in the detection of $\theta$, respectively. We show that the original optimal stopping problems can be reduced to a unifying optimal stopping problem; then, we derive the associated free-boundary problem and we provide sufficient conditions for the existence and uniqueness of its solution.

我们研究了时间均匀扩散过程的无序问题。目的是确定无序时间的有效检测策略$\theta$, 过程改变其漂移。我们专注于$\epsilon$-线性和预期的总未命中标准，其中，与众所周知的线性惩罚标准不同，早期/错误检测的预期惩罚$\theta$表示为至少发出错误警报的频率$\epsilon$之前的时间单位$\theta$并且作为检测的预期进展$\theta$， 分别。我们证明了原始的最优停止问题可以简化为一个统一的最优停止问题；然后，我们推导出相关的自由边界问题，并为其解的存在性和唯一性提供充分条件。