STOCHASTIC MODEL OF MINIMIZING OF ACHIEVABLE TERM OF GIVEN LEVEL OF POLLUTANT UTILIZATION IN MULTI-STEP ECOLOGICAL AND ECONOMIC SYSTEMS

Abstract

The research is aimed at optimizing the distribution of material resources in the economy for its simple and expanded reproduction, in particular in the case of ecological and economic interaction, as the optimal interaction of main and ancillary production in ecological and economic systems will allow to determine conditions for the optimal growth of ancillary production, which deals with the disposal of pollution. The economy, in which function the main production (production of material products) and ancillary production (disposal or destruction of pollutants), is considered. As a result of researches the stochastic model of minimization of achievable term of given level of pollutant utilization in multistep ecological and economic systems at restriction on the minimum size of irreversibility of capital investments with use of Wiener and Poisson processes is constructed. This model is investigated using the proposed sufficient optimality conditions for stochastic multi-step systems. The constructed model belongs to the class of ecological and economic models of achieving a given level of pollutant utilization in a minimum period of time. The algorithm is used to calculate the optimal process of the ecological and economic system. Аccording to this algorithm it is necessary to select a multi-tiered mode to build the optimal process and form the appropriate left, middle and right controls; calculate according to the formed controls the corresponding averages of the left, middle and right trajectories and determine the moments of switching controls; find the final moment of the planning horizon; to construct the average optimal process as gluing together at the moments of switching the controls of the averages left with the first middle, middle with each other and the last middle with the right process; calculate stochastic left, middle and right trajectories and construct stochastic left, middle and right processes; to construct a stochastic process as gluing together at the moments of switching of stochastic controls of the left process with the first middle, middle among themselves and the last middle with the right process.