Taieb Touati

Paris 1 Panthéon-Sorbonne University | UNiVPARIS1 · Départements de Mathématiques and Informatique (UFR27)

The field of concentration inequalities has gained a significant traction over the last two decades, from contributing to the resolution of complex applied problems to enhancing the theoretical framework of probability.The thesis provides a thorough and exhaustive overview of the relevant scientific literature. The two main components of this scien...

We propose new concentration inequalities for self-normalized martingales. The main idea is to introduce a suitable weighted sum of the predictable quadratic variation and the total quadratic variation of the martingale. It offers much more flexibility and allows us to improve previous concentration inequalities. Statistical applications on autoreg...