6533b837fe1ef96bd12a3474
RESEARCH PRODUCT
Generalized Wiener Process and Kolmogorov's Equation for Diffusion induced by Non-Gaussian Noise Source
Bernardo SpagnoloAlexander A. Dubkovsubject
Diffusion equationStatistical Mechanics (cond-mat.stat-mech)General MathematicsMathematical analysisGeneral Physics and AstronomyFOS: Physical sciencesOrnstein–Uhlenbeck processCondensed Matter - Soft Condensed MatterGaussian random fieldLangevin equationsymbols.namesakeStochastic differential equationAdditive white Gaussian noiseGaussian noisesymbolsProcess and Kolmogorov'sSoft Condensed Matter (cond-mat.soft)Fokker–Planck equationCondensed Matter - Statistical MechanicsMathematicsdescription
We show that the increments of generalized Wiener process, useful to describe non-Gaussian white noise sources, have the properties of infinitely divisible random processes. Using functional approach and the new correlation formula for non-Gaussian white noise we derive directly from Langevin equation, with such a random source, the Kolmogorov's equation for Markovian non-Gaussian process. From this equation we obtain the Fokker-Planck equation for nonlinear system driven by white Gaussian noise, the Kolmogorov-Feller equation for discontinuous Markovian processes, and the fractional Fokker-Planck equation for anomalous diffusion. The stationary probability distributions for some simple cases of anomalous diffusion are derived.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2005-01-01 |