Stochastic Stability

Stochastic stability analyzes the robustness of dynamical systems, particularly those subject to random disturbances, focusing on ensuring that system trajectories remain bounded or converge to a desired state despite uncertainties. Current research emphasizes developing methods to guarantee stability in various contexts, including multi-agent systems, control systems with bounded or unbounded noise, and deep generative models like flow matching and deep Markov models. These advancements are crucial for designing reliable and resilient systems in diverse applications, from robotics and autonomous control to machine learning and data-driven modeling, by providing rigorous mathematical frameworks for assessing and improving system performance under uncertainty.