6533b7d9fe1ef96bd126b971
RESEARCH PRODUCT
A method for the probabilistic analysis of nonlinear systems
Marcello VastaM. Di PaolaG. Ricciardisubject
Characteristic function (probability theory)Stochastic processMechanical EngineeringAerospace EngineeringOcean EngineeringStatistical and Nonlinear PhysicsProbability density functionCondensed Matter Physicssymbols.namesakeNonlinear systemNuclear Energy and EngineeringTaylor seriessymbolsCalculusApplied mathematicsProbabilistic analysis of algorithmsCumulantCivil and Structural EngineeringMathematicsTaylor expansions for the moments of functions of random variablesdescription
Abstract The probabilistic description of the response of a nonlinear system driven by stochastic processes is usually treated by means of evaluation of statistical moments and cumulants of the response. A different kind of approach, by means of new quantities here called Taylor moments, is proposed. The latter are the coefficients of the Taylor expansion of the probability density function and the moments of the characteristic function too. Dual quantities with respect to the statistical cumulants, here called Taylor cumulants, are also introduced. Along with the basic scheme of the method some illustrative examples are analysed in detail. The examples show that the proposed method is an attractive tool for the analysis of a wide class of stochastic systems.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1995-01-01 |