Stochastic Modeling of Technological Labor Market Dynamics with Fast Markov Switching Via the Averaging Principle

• Date: 2026
• Main Authors: Сачовська, Віталіна, Перцов, Андрій
• Format: Article
• Language: English
• Published: Кам'янець-Подільський національний університет імені Івана Огієнка 2026
• Online Access: https://mcm-math.kpnu.edu.ua/article/view/354706
• Journal Title: Mathematical and computer modelling. Series: Physical and mathematical sciences

This study considers a stochastic evolutionary representation of the technological labor market, focusing on the interaction between employment and automation in the IT sector. The dynamics are described by a nonlinear competition system of Lotka-Volterra type, extended by a rapidly switching random environment modeled through a Markov process. Such a formulation makes it possible to reflect changes in technological regimes and their influence on the structure of the labor market beyond the limitations of deterministic models. The presence of fast stochastic switching leads to analytical difficulties, which are addressed by employing an averaging approach. Assuming ergodicity of the underlying Markov process, the original stochastic system can be replaced, in the limit, by a deterministic model whose coefficients are obtained from the stationary distribution of the environment. This reduction preserves the qualitative features of the system while making its analysis more tractable. The behavior of the model is illustrated through several scenarios reflecting different technological environments, including innovative adaptation, technological polarization, and unstable regime switching. The simulation results show that, in most cases, stochastic trajectories remain concentrated near the corresponding averaged dynamics, confirming the applicability of the averaging approach. At the same time, noticeable deviations may arise in asymmetric environments with strong nonlinear effects. The developed framework can be used to investigate long-term interactions between automation and employment and to assess structural changes in the technological labor market under uncertainty.