On a control system on an infinite temporal tree

We discuss the stochastic interpretation of a control system determined by a system of differential equations on a tree. For example, such a system on a finite tree arises after replacing the coefficients of the equation on an interval with stochastic processes in discrete time and with finitely many states. The countable number of states will correspond to a more complicated and, at the same time, more general case of an infinite tree, which is under consideration.