Quickest detection of abrupt changes for a class of random processes

We consider the problem of quickest detection of abrupt changes for processes that are not necessarily independent and identically distributed (i.i.d.) before and after the change. By making a very simple observation that applies to most well-known optimum stopping times developed for this problem (in particular CUSUM and Shiryayev-Roberts (1963) stopping rule) we show that their optimality can be easily extended to more general processes than the usual i.i.d. case.