Generalized Wiener Process and Kolmogorov's Equation for Diffusion Induced by Non-Gaussian Noise Source
- Autori: DUBKOV, AA; SPAGNOLO, B
- Anno di pubblicazione: 2005
- Tipologia: Articolo in rivista (Articolo in rivista)
- Parole Chiave: Process and Kolmogorov's
- OA Link: http://hdl.handle.net/10447/17775
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.