We compute the asymptotic distribution of the maximum likelihood ratio test when we want to check whether the parameters of normal observations have changed at an unknown point. The proof is based on the limit distribution of the largest deviation between a $d$-dimensional Ornstein-Uhlenbeck process and the origin.
"The Maximum Likelihood Method for Testing Changes in the Parameters of Normal Observations." Ann. Statist. 21 (2) 671 - 680, June, 1993. https://doi.org/10.1214/aos/1176349143