Approximate moment dynamics for polynomial and trigonometric stochastic systems

Stochastic dynamical systems often contain non-linearities that make it hard to compute probability density functions or statistical moments of these systems. For the moment computations, nonlinearities lead to the well-known problem of unclosed moment dynamics, i.e., differential equations that govern the time evolution of moments up to a certain order may contain some moments of higher order. Moment closure techniques are used to find an approximate, closed system of equations for the moment dynamics, but their usage is rather limited for systems with continuous states particularly when the nonlinearities are non-polynomials. Here, we extend a moment closure technique based on derivative matching, which was originally proposed for polynomial stochastic systems with discrete states, to continuous state stochastic differential equations with both polynomial and trigonometric nonlinearities.