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

Bernardo Spagnolo, Alexander Dubkov

Risultato della ricerca: Article

73 Citazioni (Scopus)

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.
Lingua originaleEnglish
pagine (da-a)L267-L274
Numero di pagine7
RivistaFluctuation and Noise Letters
Volume5
Stato di pubblicazionePublished - 2005

    Fingerprint

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Physics and Astronomy(all)

Cita questo