Estimating parameters in SDEs using the stochastic gradient descent

Ponente(s): Francisco Javier Delgado Vences, Jose Julian Pavon-Español

In this study, we employ stochastic gradient descent to minimize a functional used for estimating parameters of stochastic differential equations (SDEs), which illustrates a primary example of an inverse problem. We utilize the Wiener chaos expansion to express the solution of stochastic differential equations (SDEs), which is a spectral decomposition in the random parameter. This approach enables us to break down the functional into a series of deterministic functions known as the propagator. Therefore, we will demonstrate its application through a selection of SDEs, accompanied by several numerical experiments.