The Stochastic Occupation Kernel Method for System Identification
This work addresses system identification for stochastic processes, offering a method to model complex dynamics, but it appears incremental as it builds on existing occupation kernel techniques for deterministic cases.
The authors tackled the problem of learning both drift and diffusion terms of a stochastic differential equation from data snapshots, proposing a two-step method that first estimates drift using occupation kernels and then diffusion via a semi-definite program, with examples and simulations demonstrating the approach.
The method of occupation kernels has been used to learn ordinary differential equations from data in a non-parametric way. We propose a two-step method for learning the drift and diffusion of a stochastic differential equation given snapshots of the process. In the first step, we learn the drift by applying the occupation kernel algorithm to the expected value of the process. In the second step, we learn the diffusion given the drift using a semi-definite program. Specifically, we learn the diffusion squared as a non-negative function in a RKHS associated with the square of a kernel. We present examples and simulations.