Simple general method to analyse the moment stability and sensitivity of non-linear stochastic systems with or without delay

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Abstract
Under broad mathematical conditions, the knowledge of the probability density p(x,t) of a non-linear stochastic system denned by an Itô stochastic differential equation is completely equivalent to the knowledge of all its state moments mi(t), and as a consequence, one can investigate analysis techniques based on the study of the former. When the non-linearities involved in the system are polynomials, these moments satisfy an infinite set of linear differential equations, a truncated version of which provides practical results. Otherwise, Galerkin's approximations are useful for reducing to the above case; and moreover they are supported by functional continuity properties. The technique applies to systems with or without delays.

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