A Lévy-driven process with matrix scaling exponent

Stochastics Seminar
Thursday, December 3, 2020 - 3:30pm for 1 hour (actually 50 minutes)
B. Cooper Boniece – Washington University in St. Louis
Cheng Mao

In the past several decades, scale invariant stochastic processes have been used in a wide range of applications including internet traffic modeling and hydrology.  However, by comparison to univariate scale invariance, far less attention has been paid to characteristically multivariate models that display aspects of scaling behavior the limit theory arguably suggests is most natural.
In this talk, I will introduce a new scale invariance model called operator fractional Lévy motion and discuss some of its interesting features, as well as some aspects of wavelet-based estimation of its scaling exponents. This is related to joint work with Gustavo Didier (Tulane University), Herwig Wendt (CNRS, IRIT Univ. of Toulouse) and Patrice Abry (CNRS, ENS-Lyon).