On Time-Varying Delayed Stochastic Differential Systems With Non-Markovian Switching Parameters

This article focuses on time-varying delayed stochastic differential systems with stochastically switching parameters formulated by a unified switching behavior combining a discrete adapted process and a Cox process. Unlike prior studies limited to stationary and ergodic switching scenarios, our research emphasizes non-Markovian, nonstationary, and nonergodic cases. It arrives at more general results regarding stability analysis with a more rigorous methodology. The theoretical results are validated through numerical examples.