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Probability and Computational Finance Seminar
Frederi G. Viens
Purdue University
Title: Comparison inequalities on Wiener space

Abstract: We define a covariance-type operator on Wiener space, which we use to extend the notion of covariance and canonical metric for vectors and random fields on Wiener space, and prove corresponding non-Gaussian comparison inequalities on Wiener space, which extend the Sudakov-Fernique result on comparison of expected suprema of Gaussian fields, and the Slepian inequality for functionals of Gaussian vectors. These results are proved using a so-called smart-path method on Wiener space, and are illustrated via various examples. We also illustrate the use of the same method by proving a Sherrington-Kirkpatrick universality result for spin systems in correlated and non-stationary non-Gaussian random media. This is joint work with Ivan Nourdin and Giovanni Peccati.

Date: Monday, February 16, 2015
Time: 4:30 pm
Location: Wean Hall 6423
Submitted by:  Solesne Bourguin