Математические модели стохастической динамики развития предприятий

The article proposes mathematical models of the stochastic dynamics of the single-factor manufacturing enterprises development through internal and external investments. Balance equations for such enterprises are formulated, describing random processes of continuous increase in output and growth of production factors. The interaction of proportional, progressive and digressive depreciation with internal and external investments is investigated. Equations are obtained to determine the equilibrium state of the enterprise and the limiting values of the factors of production are calculated. The cases of the stable progressive development of the enterprise, the suspension of its work during the re-equipment of production and the temporary crisis of production shutdown during equipment replacement are considered. The algorithm for the numerical solution of stochastic differential equations of enterprise development is constructed in accordance with the Euler–Maruyama method. For each implementation of this algorithm, the corresponding stochastic trajectories are constructed for the random function of the production factor. A variant of the method for calculating the expectation of a random function of a factor of production is developed and the corresponding differential equation is obtained for it. It is shown that the numerical solution of this equation and the average value of the function of the production factor calculated from two hundred realizations of stochastic trajectories give almost identical results. Numerical analysis of the developed models showed good compliance with the known statistical data of the production enterprise.