A moment hierarchy is the coupled family of equations obtained by applying a Markov jump-process generator to powers of the state. Nonlinear reaction propensity functions make a moment of one order depend on higher-order moments, so the hierarchy generally does not close after finitely many equations.
A moment closure replaces higher moments in a moment hierarchy by functions of retained lower moments. It converts an infinite hierarchy into a finite approximate system.
A central-moment closure sets selected high-order central moments to zero. For example, setting the third central moment of to zero gives
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