Some System Approaches to Water Resources Problems III. Optimal Control of Dam Storage

Some stochastic aspects of dam storage theory are considered in this paper. In particular optimal control based on some reliable lower estimates of unknown (uncertain) system parameters with the corresponding operational program is developed. Also, statistical equilibrium in dam storage (random) processes are analyzed and general conditions for such a phenomenon are established

On Two Selected Topics Connected with Stochastic Systems Theory

The existence and the explicit form of the minimal Markov process which contains as a component a given stationary process are established. It is shown in particular that the future/past splitting subspace of the multivariate stationary process is finite-dimensional if and only if the process has a rational spectral densities matrix. The property of being stochastically continuous is obtained as the condition for continuation of the sigma-algebras associated with a process with independent increments which usually represents a stochastic disturbance of the system considered. This property gives us the left-side continuation of the sigma-algebras in the case of the arbitrary process in a metric space