Synthesis of multivariate distributions from their moments for probabilistic dynamics

If the marginal distributions and the moments of order I and 2 of a multivariate distribution are known, one can interpolate the total distribution while conserving all these informations and keeping a large freedom on to be determined parameters of the synthesis. We can use it to conserve other characteristics of the distribution, or to enforce some criteria. This synthesis method is then applied to the calculation of distributions in the frame of probabilistic dynamics. We can obtain a system of hyperbolic POEs for the marginal distributions of the solution of the ChapmanKolmogorov equation. These POEs depend only on the dynamics of the. problem and on the formerly computed (Devooght, 1994) fust and second moments in order. The solution method of these equations refers to the properties of the Lie algebras, and the calculation of the marginal distribuuons is reduced to the one of time quadratures.