A Mori-Zwanzig and MITL Based Approach to Statistical Verification of Continuous-time Dynamical Systems*

In this work, we introduce a framework for the statistical verification of Metric Interval Temporal Logic (MITL) formulas on continuous-time dynamical systems. By considering the continuous-time Markov process associated with the dynamical system, we apply the Mori-Zwanzig method to reduce the original system to a Continuous-Time Markov Chain (CTMC). Accordingly, the MITL formulas on the original system can be reduced to MITL formulas on the CTMC. Furthermore, we propose a statistical verification algorithm for checking the MITL formulas on the CTMCand show that the original MITL formulas on the original system can be checked by this procedure.