Prof. Antoine Ayache will speak at the Stochastics and Finance Seminar Time: Tuesday, July 30, Venue: AGR Title: Almost sure approximations in Holder norms of a general stochastic process defined by a Young integral Abstract: We focus on a stochastic process Y defined by a pathwise Young integral of a general form. Thanks to the Haar basis, we connect the classical method of approximation of Y through Euler scheme and Riemann-Stieltjes sums with a new approach consisting in the use of an appropriate series representation of Y. This representation is obtained through a general compactly supported orthonormal wavelet basis. An advantage offered by the new approach with respect to the classical one is that a better almost sure rate of convergence in Holder norms can be derived, under a general chaos condition. Also, this improved rate turns out to be optimal in some situations; typically, when the integrand and integrator associated to Y are independent fractional Brownian motions with appropriate Hurst parameters. Joint work with Celine Esser and Qidi Peng.