David Nualart (Kansas University)

Title: Fractional Brownian  motion: Stochastic calculus and applications.

Abstract: The fractional Brownian motion is a centered self-similar Gaussian process with stationary increments, which depends on a parameter H in (0,1) called the Hurst index. In  this talk we will describe some basic properties of the fractional Brownian motion, and we will  present a version of the P. Levy characterization theorem. We will analyze different approaches  to construct a stochastic calculus with respect to the fractional Brownian motion, using path-wise techniques, Riemann sums  and Malliavin calculus. Some applications  in mathematical finance will be discussed.