Fractional Brownian motion

By David Nualart. 2006

133 citations recorded by the source corpus.

Fractional Brownian motion (fBm) is a centered self-similar Gaussian process with stationary increments, which depends on a parameter H �¸ (0, 1) called the Hurst index. In this note we will survey some facts about the stochastic calculus with respect to fBm using a pathwise approach and the techniques of the Malliavin calculus. Some applications in turbulence and finance will be discussed.

Subfields: Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6cbf7f79b6e588973436f9b1d03c0d0cbf441424

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Finance

1. Bozenna Pasik-Duncan
2. C. Lacaux
3. Jacek Jakubowski
4. Hermine Bierm'e
5. Tyrone E. Duncan

In Mathematical Physics

1. C. Lacaux
2. Bozenna Pasik-Duncan
3. Jacek Jakubowski
4. Hermine Bierm'e
5. Tyrone E. Duncan

Citations in the corpus

• Hölder regularity for operator scaling stable random fields (2007, background): “It is an isotropic generalization of the famous fractional Brownian motion, implicitely introduced in [12] and defined in [19].”
• STOCHASTIC INTEGRATION FOR FRACTIONAL BROWNIAN MOTION IN A HILBERT SPACE (2006, methodology): “In a finite dimensional Euclidean space these processes were introduced by Kolmogorov [10] and some properties of these processes were given by Mandelbrot and van Ness [13].”