Stability of the neoclassical growth model under perturbations of the type of Poisson’s jumps: Analytical and numerical analysis

Abstract

The well known delay differential neoclassical growth model is considered under stochastic perturbations of the type of Poisson’s jumps. Stability conditions for positive and the zero equilibria of this model are obtained via the Gikhman and Skorokhod theory of stochastic differential equations with the Poisson measure and the general method of Lyapunov functionals construction. The obtained analytical results are illustrated by detail numerical simulations of solutions of the considered stochastic differential equation and construction of appropriate stability regions.