Search results for "Lévy white noise"

showing 4 items of 4 documents

Stochastic analysis of external and parametric dynamical systems under sub-Gaussian Levy white-noise

2008

In this study stochastic analysis of non-linear dynamical systems under α-stable, multiplicative white noise has been conducted. The analysis has dealt with a special class of α-stable stochastic processes namely sub-Gaussian white noises. In this setting the governing equation either of the probability density function or of the characteristic function of the dynamical response may be obtained considering the dynamical system forced by a Gaussian white noise with an uncertain factor with α/2- stable distribution. This consideration yields the probability density function or the characteristic function of the response by means of a simple integral involving the probability density function …

Mathematical optimizationDynamical systems theoryCharacteristic function (probability theory)Stochastic processMechanical EngineeringFokker-Planck equationProbability density functionLévy white noiseBuilding and ConstructionWhite noiseStable processstochastic differential calculusymbols.namesakeAdditive white Gaussian noiseMechanics of MaterialssymbolsStatistical physicssub-Gaussian white noise.Settore ICAR/08 - Scienza Delle CostruzioniRandom dynamical systemCivil and Structural EngineeringMathematicsStructural Engineering and Mechanics
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First-passage problem for nonlinear systems under Lévy white noise through path integral method

2016

In this paper, the first-passage problem for nonlinear systems driven by $$\alpha $$ -stable Levy white noises is considered. The path integral solution (PIS) is adopted for determining the reliability function and first-passage time probability density function of nonlinear oscillators. Specifically, based on the properties of $$\alpha $$ -stable random variables and processes, PIS is extended to deal with Levy white noises with any value of the stability index $$\alpha $$ . Application to linear and nonlinear systems considering different values of $$\alpha $$ is reported. Comparisons with pertinent Monte Carlo simulation data demonstrate the accuracy of the results.

Mathematical optimizationPath integralMonte Carlo methodAerospace Engineering020101 civil engineeringOcean EngineeringProbability density function02 engineering and technologyLévy white noise0201 civil engineering0203 mechanical engineeringApplied mathematicsElectrical and Electronic EngineeringMathematicsFirst passageApplied MathematicsMechanical EngineeringWhite noiseFunction (mathematics)Nonlinear systemAlpha (programming language)020303 mechanical engineering & transportsControl and Systems EngineeringPath integral formulationNonlinear systemRandom variable
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Stochastic response of linear and non-linear systems to α-stable Lévy white noises

2005

Abstract The stochastic response of linear and non-linear systems to external α -stable Levy white noises is investigated. In the literature, a differential equation in the characteristic function (CF) of the response has been recently derived for scalar systems only, within the theory of the so-called fractional Einstein–Smoluchowsky equations (FESEs). Herein, it is shown that the same equation may be built by rules of stochastic differential calculus, previously applied by one of the authors to systems driven by arbitrary delta-correlated processes. In this context, a straightforward formulation for multi-degree-of-freedom (MDOF) systems is also developed. Approximate CF solutions to the …

Non-Gaussian inputDifferential equationMechanical EngineeringCharacteristic equationAerospace EngineeringOcean EngineeringStatistical and Nonlinear PhysicsDifferential calculusWhite noiseCondensed Matter PhysicsMethod of mean weighted residualsNonlinear systemStochastic differential equationExact solutions in general relativityNuclear Energy and EngineeringCalculusApplied mathematicsα-stable Lévy white noiseStochastic differential calculusCivil and Structural EngineeringMathematics
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Nonlinear SDE Excited by External Lévy White Noise Processes

2011

A numerical method for approximating the statistics of the solution of nonlinear stochastic systems excited by Gaussian and non-Gaussian external white noises is proposed. The differential equation governing the evolution in time of the characteristic function is resolved by the convolution quadrature method. This approach is especially suited for those problems in which the nonlinear drift term is not of polynomial form. In such cases the equation governing the evolution in time of the characteristic function is not a partial differential equation. Statistics are found by introducing an integral operator of Wiener-Hopf type, called the transformation operator, and applying the Lubich's con…

PhysicsNonlinear systemConvolution quadrature: Lévy white noiseStochastic differential equationExcited stateQuantum electrodynamicsNon-polynomial drift.White noiseSettore ICAR/08 - Scienza Delle CostruzioniGeneralized fractional calculuProceedings of the 6th International Conference on Computational Stochastic Mechanics(CSM-6)
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