Abstract
In this paper, a Brownian motion of order n is defined by a probabilistic approach which is different from Mandelbrot's and Sainty's models. This process is constructed in the form of the integral of a complex Gaussian white noise which itself is defined as the product of a Gaussian white noise by a complex white process which takes on values on the set of the roots of the unity of order n. An Itô-Taylor's lemma of order n is obtained; therefore one derives the dynamical equations of the complex Brownian motion moments whereby one can obtain a generalized Fokker-Planck equation or heat equation of order n. A possible relation with Kramers-Moyal expansion is outlined. The framework is essentially applied mathematics.
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Schedule a callMore From: Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena
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