Moment closure for FV-processes using moment-generating functions

Abstract

Understanding stochastic processes by calculating their moments, is a relevant task for an unfathomable number of real-world applications. For finite variation processes with non-linear dynamics, the calculation of moments is notoriously difficult due to the infinite system of moment equations that has to be solved approximately. Moment closure techniques that truncate the infinite system of moment equations has been studied since the sixties, and is to this day an active area of research. Instead of approximating the moments directly through the moment equations, we propose to approximate the moment-generating function, based on a derivation of the PDE for the moment-generating function involving infinite partial derivatives. We construct a finite difference scheme that approximates the moment-generating function, and conduct a numerical study to verify its use.

Keywords: Projection; Infinite PDEs; Polynomial dynamics; Moment truncation