Search results for " Fractional moments"

showing 5 items of 5 documents

On the use of fractional calculus for the probabilistic characterization of random variables

2009

In this paper, the classical problem of the probabilistic characterization of a random variable is re-examined. A random variable is usually described by the probability density function (PDF) or by its Fourier transform, namely the characteristic function (CF). The CF can be further expressed by a Taylor series involving the moments of the random variable. However, in some circumstances, the moments do not exist and the Taylor expansion of the CF is useless. This happens for example in the case of $\alpha$--stable random variables. Here, the problem of representing the CF or the PDF of random variables (r.vs) is examined by introducing fractional calculus. Two very remarkable results are o…

Characteristic function (probability theory)FOS: Physical sciencesAerospace EngineeringMathematics - Statistics TheoryOcean EngineeringProbability density functionComplex order momentStatistics Theory (math.ST)Fractional calculusymbols.namesakeIngenieurwissenschaftenFOS: MathematicsTaylor seriesApplied mathematicsCharacteristic function serieMathematical PhysicsCivil and Structural EngineeringMathematicsGeneralized Taylor serieMechanical EngineeringStatistical and Nonlinear PhysicsProbability and statisticsMathematical Physics (math-ph)Condensed Matter PhysicsFractional calculusFourier transformNuclear Energy and EngineeringPhysics - Data Analysis Statistics and ProbabilitysymbolsFractional calculus; Generalized Taylor series; Complex order moments; Fractional moments; Characteristic function series; Probability density function seriesddc:620Series expansionFractional momentProbability density function seriesSettore ICAR/08 - Scienza Delle CostruzioniRandom variableData Analysis Statistics and Probability (physics.data-an)
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CROSS-POWER SPECTRAL DENSITY AND CROSS-CORRELATION REPRESENTATION BY USING FRACTIONAL SPECTRAL MOMENTS

2012

Fractional calculus Mellin transform Complex order moments Fractional moments Fractional spectral moments Cross-correlation function Cross-power spectral density function
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Probabilistic characterization of nonlinear systems under α-stable white noise via complex fractional moments

2015

Abstract The probability density function of the response of a nonlinear system under external α -stable Levy white noise is ruled by the so called Fractional Fokker–Planck equation. In such equation the diffusive term is the Riesz fractional derivative of the probability density function of the response. The paper deals with the solution of such equation by using the complex fractional moments. The analysis is performed in terms of probability density for a linear and a non-linear half oscillator forced by Levy white noise with different stability indexes α . Numerical results are reported for a wide range of non-linearity of the mechanical system and stability index of the Levy white nois…

Statistics and ProbabilityFractional Fokker-Planck equationα-stable white noiseMathematical analysisProbabilistic logicStatistical and Nonlinear PhysicsProbability density functionCondensed Matter PhysicWhite noiseComplex fractional momentStability (probability)Fractional calculusMechanical systemNonlinear systemNonlinear systemRange (statistics)Complex fractional moments; Fractional Fokker-Planck equation; Nonlinear systems; α-stable white noise; Condensed Matter Physics; Statistics and ProbabilityMathematicsPhysica A: Statistical Mechanics and its Applications
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Einstein-Smoluchowsky equation handled by complex fractional moments

2014

In this paper the response of a non linear half oscillator driven by α-stable white noise in terms of probability density function (PDF) is investigated. The evolution of the PDF of such a system is ruled by the so called Einstein-Smoluchowsky equation involving, in the diffusive term, the Riesz fractional derivative. The solution is obtained by the use of complex fractional moments of the PDF, calculated with the aid of Mellin transform operator. It is shown that solution can be found for various values of stability index α and for any nonlinear function of the drift term in the stochastic differential equation.

Stochastic partial differential equationNonlinear systemStochastic differential equationMellin transformDifferential equationOperator (physics)Mathematical analysisProbability density functiona-stable white noise Nonlinear systems Einstein-Smoluchowsky equation Complex fractional momentsFractional calculusMathematics
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Probabilistic characterization of nonlinear systems under parametric Poisson white noise via complex fractional moments

2014

nonlinear systems Poisson white noise fractional moments
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