Nonparametric inference of stochastic differential equations based on the relative entropy rate

The information detection of complex systems from data is currently undergoing a revolution, driven by the emergence big and machine learning methodology. Discovering governing equations quantifying dynamical properties are among central challenges. In this work, we devised nonparametric approach to relative entropy rate observations stochastic differential with different drift functions. estimator corresponding then presented via Gaussian process kernel theory. Meanwhile, enables us extract equations. We illustrate our several examples. Numerical experiments show proposed performs well for rational functions, not only polynomial