Tim Fuchs: Upper and Lower Bounds for Suprema of Chaos Processes

Abstract:

There are diverse techniques of analyzing a stochastic process. In the following, Talagrand's generic chaining will be introduced and bounds for the expected supremum of different stochastic processes proved.

The main focus lies on a result of Krahmer, Mendelson and Rauhut who were able to prove an alternative inequality for a specic kind of chaos process. As this bound leads to signicantly better results in some applications, the sharpness of this inequality and a possible improvement will be investigated.