A new approach to complex-valued fractional Brownian motion via rotating white noise

✍ Scribed by Guy Jumarie

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 681 KB
• Volume: 9
• Category: Article
• ISSN: 0960-0779
• DOI: 10.1016/s0960-0779(97)00173-2

✦ Synopsis

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 It&-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.