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Stochastic dynamical systems often contain nonlinearities which make it hardto compute probability density functions or statistical moments of thesesystems. For the moment computations, nonlinearities in the dynamics lead tounclosed moment dynamics; in particular, the time evolution of a moment of aspecific order may depend both on moments of order higher than it and on somenonlinear function of other moments. The moment closure techniques are used tofind an approximate, close system of equations the moment dynamics. In thiswork, we extend a moment closure technique based on derivative matching thatwas originally proposed for polynomial stochastic systems with discrete statesto continuous state stochastic systems to continuous state stochasticdifferential equations, with both polynomial and trigonometric nonlinearities.We validate the technique using two examples of nonlinear stochastic systems.

Approximate moment dynamics for polynomial and trigonometric stochastic systems