This article is cited in 3 papers

Moments methods for analytical modeling of stochastic systems on manifolds

I. N. Sinitsyn

Institute of Informatics Problems, Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation

Abstract: Problems of accuracy and sensitivity estimation for algorithms of analytical modeling methods (AMM) based on one- and multidimensional initial moments methods (IMM) and central moments method (CMM) in stochastic systems on manifolds (MStS) with Wiener and Poisson noises are considered. For typical reliability and security problems accuracy and sensitivity, equations for AMM are given. Problems of reduction of equations for IMM and CMM are discussed. The results are the basis of symbolic software tools in MATLAB-MAPLE. A test example for scalar MStS with cubic nonlinearity and multiplicative Gaussian noise is given. Some generalizations are presented.

Keywords: accuracy IMM and CMM equations; analytical modeling method (AMM); central moments method (CMM); Hermite polynomials; initial moments method (IMM); one- and multidimensional distribution density; sensitivity IMM and CMM equations; stochastic system on manifold (MStS).

Received: 12.08.2015

DOI: 10.14357/08696527150302

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