Numerical Study of Stochastic Leontief-Type Model with Impulses

Abstract

ABSTRACT In this article, a stochastic Leontief model with impulses has been studied, which is represented by a system of stochastic differential-algebraic equations, in both sides of the rectangular constant numerical matrices that form a singular pencil. The system has been considered in terms of the current velocity of the solution, which is a direct analog of the physical velocity of deterministic processes. The proposed approach in this work does not impose restrictions on the size and the form of the matrices included in the Leontief-type system. The Kroenke-Weierstrass transformation of the pencil was conducted by the coefficient matrices to the canonical form has been used to simplify the study of equations. This study also involves two methods: Firstly, using a stochastic differential equation, this was followed by using the so-called mean derivatives of Nelson random processes to describe the solutions of this equation. The distinguishing feature of the work proposed an approach based on the convergence of the theoretical results to the exact one. The findings show that explicit formulas for solutions and solvability conditions are obtained, and for a subsystem resolved with respect to the symmetric derivative. The theorem of existence of solutions for the system under consideration has been proved under certain conditions on the coefficients of the system. Conducting computational experiments on the model confirming the effectiveness of the proposed approach. Error, maximum and minimum of the singular values of matrices.