Using MLE for parameter estimation of a one-dimensional Ornstein–Uhlenbeck process is widely known. However, has a similar work been done of a process on the form
\begin{equation} X_t = \min \left( \int_0^t \theta (X_t - \mu) \, dt + \int_0^t \sigma \, dB_t , \alpha\right) \text{?} \end{equation}
This is in the context of capped mean-reversing process. I.e, given data from that process, what does MLE look like to estimate the parameters $\Theta = (\theta, \mu, \sigma)$?
