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Analysis of Nonlinear Stochastic Distributed Systems by using the Dynamic Equations of their State Moments

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1 Author(s)
Guy Jumarie ; Dept of Mathematics and Computer Science, Université du Québec, à Montréal; P.O. Box 8888, St A; Montréal, QUE, H3C 3P8; Canada

Under large mathematical conditions, the kowledge of the state probability density of a nonlinear stochastic distributed system is completely equivalent to the knowledge of all its state moments; and as a consequence, it may be interesting to investigate analysis techniques based on the study of these moments only. A method is herein proposed, which avoids the use of stochastic partial differential equations but rather defines the system by its infinitesimal transition moments. When the nonlinearities so involved by the system are polynomials with respect to the state, then the state moments satisfy an infinite set of linear differential integral equations. When such is not the case, then Galerkin's approximations are useful, and this approach is supported by functional continuity properties.

Published in:

American Control Conference, 1987

Date of Conference:

10-12 June 1987