A stochastic model of a single-product growth economy with endogenous scientific and technological progress under investment lag with Wiener and Poisson processes is proposed. In the stochastic economic-mathematical model it is taken into account that the final output is used for consumption, for investment in the expansion of fixed assets, for improving production, taking into account the cost-effectiveness of "science", for taxation, for government expenditures, for the balance and for the elimination of environmental pollution. This model takes into account the impact of research on economic production in the system itself, i.e. this impact is an endogenous variable. Stochastic sufficient conditions of optimality are used to study the stochastic optimal ecological-economic model An algorithm for calculating the optimal process when choosing the necessary economic boundary mode at the initial stage, as well as an algorithm for calculating the optimal process when choosing the economic main mode when choosing at the initial stage, is constructed.