Fractional Brownian motion: stochastic calculus and applications
David Nualart
University of Kansas, Lawrence, USA
![Fractional Brownian motion: stochastic calculus and applications cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fbooks%2Fcover-24.png&w=3840&q=90)
Download Chapter PDF
A subscription is required to access this book chapter.
Abstract
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.