Approximate moment dynamics for polynomial and trigonometric stochastic systems

TL;DR

This paper extends a derivative matching moment closure technique from discrete to continuous stochastic systems with polynomial and trigonometric nonlinearities, enabling approximate computation of moments in complex nonlinear stochastic dynamics.

Contribution

The work introduces a novel extension of derivative matching moment closure to continuous stochastic differential equations with polynomial and trigonometric nonlinearities.

Findings

Validated the technique on nonlinear stochastic systems

Demonstrated accurate approximation of moments

Extended applicability to continuous state systems

Abstract

Stochastic dynamical systems often contain nonlinearities which make it hard to compute probability density functions or statistical moments of these systems. For the moment computations, nonlinearities in the dynamics lead to unclosed moment dynamics; in particular, the time evolution of a moment of a specific order may depend both on moments of order higher than it and on some nonlinear function of other moments. The moment closure techniques are used to find an approximate, close system of equations the moment dynamics. In this work, we extend a moment closure technique based on derivative matching that was originally proposed for polynomial stochastic systems with discrete states to continuous state stochastic systems to continuous state stochastic differential equations, with both polynomial and trigonometric nonlinearities. We validate the technique using two examples of nonlinear stochastic systems.