Stochastics and Finance Seminar: Antoine Ayache -- Stochastic analysis

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.