Can the averaging principle be extended to stochastic systems? This research expands upon Anosov's and Neistadt's theorems, applying them to stochastic differential equations representing fast and slow motions. This study builds upon prior deterministic models, now addressing stochastic scenarios. The study focuses on systems where slow motion approximations are derived by averaging parameters in fast variables. The findings extend to scenarios with stochastic differential equations, enhancing the applicability of the averaging principle. These results advance the understanding of systems exhibiting both slow and fast motions. It is particularly relevant in fields such as physics and engineering, where stochastic models are used to represent complex dynamics.
This article, published in Stochastics and Dynamics, fits the journal's focus on stochastic processes and dynamical systems. By extending classical theorems to stochastic settings, it contributes to the mathematical foundations of these fields.