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 KolmogorovFeller 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.
|Numero di pagine||7|
|Rivista||Fluctuation and Noise Letters|
|Stato di pubblicazione||Published - 2005|
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