Moment closure

In nonlinear stochastic models, equations for lower moments often depend on higher moments. The resulting hierarchy may not close after finitely many equations.

For example, an equation for a mean can involve a second moment, whose equation can involve a third moment, and so on.

Closure approximation

Moment closure replaces selected higher moments by approximations expressed using lower moments. The particular approximation depends on assumptions about the distribution or dependence structure.

Limitation

Closure introduces approximation error and should be checked against simulation or other evidence when possible.