Maxima of Gaussian Processes and Applications

Date Time Room
11.04.2011 08:00-10:00 ETHZ, HG G 19.2
12.04.2011 08:00-12:00 PLD-E-04
13.04.2011 08:00-10:00 PLD-E-04
14.04.2011 08:00-10:00 / 13:00-15:00 ETHZ, HG G 19.2
15.04.2011 10:00-12:00 / 14:00-16:00 PLD-E-04

Contents

  • Definition of stochastic processes
  • Gaussian distribution and Gaussian processes
  • Regularity of the paths
  • Basis inequalities: Plackett-Slepian, Borell Sudakov Tsirelson
  • Rice formulas for the number of crossings of a process. Gaussian and non Gaussian case
  • Basis bounds for the distribution of the maximum of a Gaussian process
  • Application to change points detection
  • Application to gene detection
  • Computation of Gaussian integrals in high dimension by Monte-Carlo Quasi-Monte-Carlo (MCQMC) method
  • Application to the prediction of electrical load curves
  • Rice formula for random fields
  • Application to the record method
  • Application to roots of random polynomials

Grading

Based on take-home exam

Credits

3 ECTS for all tracks

Course outline