Stability in distribution of nonlinear hybrid stochastic systems with non-differentiable time delays

This paper delves into the analysis of a category of highly nonlinear hybrid stochastic systems with non-differentiable time delays, which has caught the attention of scholars in recent years due to its relevance to real-world applications. As an essential step in studying stochastic systems, a generalized Hasminskii-type theorem is initially formulated for the existence and uniqueness of the global solution. The central focus lies on addressing the crucial issue of stability in distribution. To this end, the paper presents several significant lemmas to examine the stability in distribution of this system and proposes some sufficient conditions. An example is provided to validate the accuracy and validity of the theoretical results.