Data-Driven Estimation of Infinitesimal Generators of Stochastic Systems

This paper is concerned with a data-driven approach for the estimation of infinitesimal generators continuous-time stochastic systems unknown dynamics. We first approximate generator solution process via set data collected from trajectories system. The approximation utilizes both time discretization and sampling process. Assuming proper continuity assumptions on dynamics system, we then quantify closeness between its while providing priori guaranteed confidence bound. demonstrate that number play significant roles in reasonable precision. Moreover, fixed size data, variance converges to infinity when parameter goes zero. formulated error bound shows how pick jointly prevent this counter-intuitive behavior. proposed results are demonstrated case study.