Analysis of moment stability and sensitivity of non-linear stochastic distributed systems: a practical approach via a distributed Fokker-Planck equation

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Abstract
A Fokker-Planck equation for a class of stochastic distributed systems, described by a distributed probability density p(.x,z,l) is derived. These processes are defined by their first two transition moments expressed in terms of Green's functions; and by using very simple assumptions, one can write the equations of the state moments themselves, therefore the Fokker-Planck equation. The main interest of this approach is to avoid the problem of seeking the probability density of the transition as well as the use of the Chapman-Kolmogorov equation. This is a statistical viewpoint stressing the absence of the stochastic differential equation. The equations of the stale moments are then used to analyse the stability and the sensitivity of the stochastic distributed system.

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