6533b857fe1ef96bd12b4eb5
RESEARCH PRODUCT
A novel exact representation of stationary colored Gaussian processes (fractional differential approach)
Giulio CottoneGiulio CottoneMario Di PaolaRoberta Santorosubject
FOS: Computer and information sciencesStatistics and ProbabilityDifferential equationFOS: Physical sciencesGeneral Physics and AstronomyStatistics - ComputationStochastic differential equationsymbols.namesakeSpectral MomentsApplied mathematicsStationary processeGaussian processCondensed Matter - Statistical MechanicsComputation (stat.CO)Mathematical PhysicsMathematicsGeneralized functionStatistical Mechanics (cond-mat.stat-mech)Statistical and Nonlinear PhysicsMathematical Physics (math-ph)White noiseClosed and exact differential formsColors of noiseGaussian noiseFractional CalculuModeling and SimulationsymbolsSettore ICAR/08 - Scienza Delle Costruzionidescription
A novel representation of functions, called generalized Taylor form, is applied to the filtering of white noise processes. It is shown that every Gaussian colored noise can be expressed as the output of a set of linear fractional stochastic differential equations whose solution is a weighted sum of fractional Brownian motions. The exact form of the weighting coefficients is given and it is shown that it is related to the fractional moments of the target spectral density of the colored noise.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2010-01-01 |