Search results for " Kolmogorov-Feller"

showing 3 items of 3 documents

Multiplicative cases from additive cases: Extension of Kolmogorov–Feller equation to parametric Poisson white noise processes

2007

Abstract In this paper the response of nonlinear systems driven by parametric Poissonian white noise is examined. As is well known, the response sample function or the response statistics of a system driven by external white noise processes is completely defined. Starting from the system driven by external white noise processes, when an invertible nonlinear transformation is applied, the transformed system in the new state variable is driven by a parametric type excitation. So this latter artificial system may be used as a tool to find out the proper solution to solve systems driven by parametric white noises. In fact, solving this new system, being the nonlinear transformation invertible, …

Fokker-Planck equation; Itô's calculus; Kolmogorov-Feller equation; Parametric forces; Poisson input; Stochastic differential calculusState variableAerospace EngineeringOcean EngineeringKolmogorov-Feller equationPoisson inputlaw.inventionlawCivil and Structural EngineeringMathematicsParametric statisticsParametric forceMechanical EngineeringMathematical analysisFokker-Planck equationStatistical and Nonlinear PhysicsWhite noiseCondensed Matter PhysicsItô's calculuNonlinear systemNoiseInvertible matrixNuclear Energy and EngineeringFokker–Planck equationStochastic differential calculusPoisson's equationProbabilistic Engineering Mechanics
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Non-linear Systems Under Poisson White Noise Handled by Path Integral Solution

2008

An extension of the path integral to non-linear systems driven by a Poissonian white noise process is presented. It is shown that at the limit when the time increment becomes infinitesimal the Kolmogorov— Feller equation is fully restored. Applications to linear and non-linear systems with different distribution of the Dirac's deltas occurrences are performed and results are compared with analytical solutions (when available) and Monte Carlo simulation.

Mechanical EngineeringInfinitesimalMathematical analysisMonte Carlo methodAerospace EngineeringWhite noisePoisson distributionPoisson White Noise Kolmogorov-Feller equation Path integral solution.Nonlinear systemsymbols.namesakeDistribution (mathematics)Mechanics of MaterialsAutomotive EngineeringPath integral formulationsymbolsGeneral Materials ScienceLimit (mathematics)Settore ICAR/08 - Scienza Delle CostruzioniMathematicsJournal of Vibration and Control
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Probabilistic characterization of nonlinear systems under Poisson white noise via complex fractional moments

2014

In this paper, the probabilistic characterization of a nonlinear system enforced by Poissonian white noise in terms of complex fractional moments (CFMs) is presented. The main advantage in using such quantities, instead of the integer moments, relies on the fact that, through the CFMs the probability density function (PDF) is restituted in the whole domain. In fact, the inverse Mellin transform returns the PDF by performing integration along the imaginary axis of the Mellin transform, while the real part remains fixed. This ensures that the PDF is restituted in the whole range with exception of the value in zero, in which singularities appear. It is shown that using Mellin transform theorem…

Mellin transformApplied MathematicsMechanical EngineeringMonte Carlo methodMathematical analysisProbabilistic logicAerospace EngineeringOcean EngineeringProbability density functionWhite noiseComplex fractional moment Kolmogorov-Feller Mellin transform Poisson white noise Probability density functionNonlinear systemLinear differential equationControl and Systems EngineeringMellin inversion theoremElectrical and Electronic EngineeringMathematics
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