Monitoring, or runtime verification, is a lightweight formal verification technique that analyzes individual executions rather than exploring the entire state space. In this talk, I will present one approach to monitoring in the context of STARK. Specifically, we consider DisTL, a logic for expressing properties about expected behavior of systems under uncertainty. Since the evaluation of DisTL formulae yields real numbers, monitoring in this setting must be quantitative. We define functions that serve as monitors for DisTL formulae under real-valued semantics and establish some of their monitoring properties.