Seminar Details

Seminar Details


Feb 2

2:30 pm

Empirical Processes and p-Variation

Dick Dudley


Massachusetts Institute of Technology - Department of Mathematics

Probability Seminar

A class of norms, the p-variation norms, give Frechet differentiability, with optimal remainder bounds, for several natural operators on functions of a real variable, including composition, convolution, the inverse (quantile) operator, (F,G) maps to smallint F dG, and (as shown in recent joint work with Rimas Norvaisa) the product integral. Some (but not all) stochastic integrals can be written as deterministic integrals when neither F nor G has bounded 1-variation.

My 1994 student Yen-Chin Huang found a sharp rate of convergence of the classical empirical process to the Brownian bridge in p-variation for p > 2, and my 1997 student Jinghua Qian found a sharp rate of convergence of Fn-F to 0 in p-variation for p < 2.