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

Alexander Dubkov; Bernardo Spagnol

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arXiv · cond-mat/0505270

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

Alexander Dubkov·Bernardo Spagnol

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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 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.

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BibTeX RIS

Alexander Dubkov, Bernardo Spagnol. 2005-05-11. Generalized Wiener Process and Kolmogorov's Equation for Diffusion induced by Non-Gaussian Noise Source. https://arxiv.org/abs/cond-mat/0505270

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