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 $\theta$ the random moment at which the density $f_0$ changes to $f_1$ (§ 1–3) or to one of the $f_1,\dots,f_m$ (§ 5). In the case when the densities $f_0,f_1,\dots,f_m$ 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.