Colloquium - Alex Schied - Fractal functions as rough integrators
Speaker: Alex Schied (University of Waterloo)
Title: Fractal functions as rough integrators
Abstract: Rough trajectories, such as the price evolution of a risky asset or other phenomena, are usually described by stochastic processes, an approach which is often subject to significant model uncertainty. In a number of situations, model uncertainty can be reduced by working with pathwise higher-order calculus that does not require any probabilistic assumptions. In the first part of this talk, we show how certain classes of fractal functions can be used as rough integrators in pathwise calculus. In the second part, we study some geometric properties of such fractal functions. We illustrate in particular that the maxima of the Takagi-Landsberg functions are connected to certain roots of Littlewood polynomials. This talk includes joint work with Xiyue Han, Yuliya Mishura, and Zhenyuan Zhang.
Coffee and Cookies will be served in the lounge (Hamilton Hall 216) at 3:00 pm. Everyone is welcome.