SPA Seminar: Approximation of stochastic integrals driven by fractional Brownian, with discontinuous integrands

Abstract: We are concerned with the approximation error of a class of stochastic integrals driven by a fractional Brownian motion with Hurst index $H>\frac{1}{2}$. In the case where the integrand verifies some adequate regularity properties, the scaling and limit behavior of the error are already relatively well understood. However, when the integrand is a discontinuous function of the fractional Brownian motion, classic tools from Young theory and Malliavin calculus no longer applies.

In this talk, we will adress this issue thanks to a fine analysis of the covariance function of the increments of the fractional Brownian motion, thus obtaining first and second order rates of convergence, as well as a limit for the error involving the local time of the fractional Brownian motion.

This is a seminar in our seminar series on Stochastic Pocesses and Applications (SPA).