Fractional Brownian motion: stochastic calculus and applications

  • David Nualart

    University of Kansas, Lawrence, USA
Fractional Brownian motion: stochastic calculus and applications cover

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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.