A METHOD FOR THE PROBABILISTIC ANALYSIS OF NONLINEAR-SYSTEMS

The probabilistic description of the response of a nonlinear system dr iven by stochastic processes is usually treated by means of evaluation of statistical moments and cumulants of the response. A different kin d of approach, by means of new quantities here called Taylor moments, is proposed. The latter are the coefficients of the Taylor expansion o f the probability density function and the moments of the characterist ic function too. Dual quantities with respect to the statistical cumul ants, here called Taylor cumulants, are also introduced. Along with th e basic scheme of the method some illustrative examples are analysed i n detail. The examples show that the proposed method is an attractive tool for the analysis of a wide class of stochastic systems.