Search results for "Path Integral method"

showing 3 items of 3 documents

Path integral method for first-passage probability determination of nonlinear systems under levy white noise

2015

In this paper the problem of the first-passage probabilities determination of nonlinear systems under alpha-stable Lévy white noises is addressed. Based on the properties of alpha-stable random variables and processes, the Path Integral method is extended to deal with nonlinear systems driven by Lévy white noises with a generic value of the stability index alpha. Furthermore, the determination of reliability functions and first-passage time probability density functions is handled step-by-step through a modification of the Path Integral technique. Comparison with pertinent Monte Carlo simulation reveals the excellent accuracy of the proposed method.

Nonlinear systemPath integral formulationCalculusNonlinear systemApplied mathematicsWhite noiseLevy white noiseSettore ICAR/08 - Scienza Delle CostruzioniFirst-passageMathematicsPath Integral method
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Path integral solution by fractional calculus

2008

In this paper, the Path Integral solution is developed in terms of complex moments. The method is applied to nonlinear systems excited by normal white noise. Crucial point of the proposed procedure is the representation of the probability density of a random variable in terms of complex moments, recently proposed by the first two authors. Advantage of this procedure is that complex moments do not exhibit hierarchy. Extension of the proposed method to the study of multi degree of freedom systems is also discussed.

HistoryComplex momentsHierarchy (mathematics)Mathematical analysisProbability density functionNon-linear Random VibrationWhite noisePath integral methodComputer Science ApplicationsEducationFractional calculusNonlinear systemPath integral formulationRepresentation (mathematics)Settore ICAR/08 - Scienza Delle CostruzioniRandom variableMathematics
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Ship Roll Motion under Stochastic Agencies Using Path Integral Method

2009

The response of ship roll oscillation under random ice impulsive loads modeled by Poisson arrival process is very important in studying the safety of ships navigation in cold regions. Under both external and parametric random excitations the evolution of the probability density function of roll motion is evaluated using the path integral (PI) approach. The PI method relies on the Chapman-Kolmogorov equation, which governs the response transition probability density functions at two close intervals of time. Once the response probability density function at an early close time is specified, its value at later close time can be evaluated. The PI method is first demonstrated via simple dynamica…

Poisson arrival proceRoll oscillationOscillationDynamics (mechanics)Motion (geometry)Probability density functionPath integral methodWhite noiseWhite noise excitationResponse amplitude operatorRandom excitationControl theoryShip roll motionTransition probabilitiePath integral formulationChapman-Kolmogorov equationMathematicsParametric statistics
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