Chaining and the Geometry of Stochastic Processes

Abstract

Kolmogorov introduced a very powerful method called chaining in order to provide bounds for the supremum of a stochastic process. Even in the case of Gaussian processes, this method has reached its seemingly nal form only about 10 years ago. When used optimally in the case of Gaussian processes, it then yields optimal bounds. We explain why we believe that this is also true in many more cases.