The question of finding Markov sufficient statistics (see definition 3) in the problem of minimisation of the functional (2) is considered. It is supposed that the parameter $\theta $ is the random moment at which the density $f_0 $ changes to $f_1 $ (§ 1–3) or to one of the $f_1 , \cdots ,f_m $ (§ 5). In the case when the densities $f_0 ,f_1 , \cdots ,f_m $ belong to the exponential family and the functional which is minimized is a non-additive one of a special form, we find a finite number of Markov sufficient statistics. Connections between the problem considered and other problems of sequential analysis are also discussed.