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BERNARDO SPAGNOLO

Generalized Wiener Process and Kolmogorov's Equation for Diffusion Induced by Non-Gaussian Noise Source

  • Authors: DUBKOV, AA; SPAGNOLO, B
  • Publication year: 2005
  • Type: Articolo in rivista (Articolo in rivista)
  • Key words: Process and Kolmogorov's
  • OA Link: http://hdl.handle.net/10447/17775

Abstract

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.