Parameter estimation with forward operators

We propose a new parameter estimation technique for SDEs, based on the inverse problem of finding a forward operator describing the evolution of temporal data. Nonlinear dynamical systems on a state-space can be lifted to linear dynamical systems on spaces of higher, often infinite, dimension. Recently, much work has gone into approximating these higher-dimensional systems with linear operators calculated from data, using what is called Dynamic Mode Decomposition (DMD). For SDEs, this linear system is given by a second-order differential operator, which we can quickly calculate and compare to the DMD operator.