Time: 10:00-11:00, Friday, October 23, 2026

Venue: Guoshun Campus, Room 303, Starr Building

Speaker: Professor Ana Ferreira, Lisbon Technology University, Portugal

Moderator: Professor Deyuan Li, Department of Statistics and Data Science, School of Management, Fudan University

Topic: Extremes at small times through ordered values of Poisson point processes

Abstract: We introduce the behaviour of large values of extremal processes at small times, through a representation of ordered values of Poisson point processes. An analogue of the Fisher-Tippet-Gnedenko Theorem allows to establish necessary and sufficient conditions for local convergence of such maxima linearly normalized. This encompasses extremes of pure jump processes with infinite activity (Levy measure). Moreover, assuming second order regular variation conditions, an adaptation of Hill's estimator of the tail index to the small time setting is established along its asymptotic normality. This provides a new formulation arising from Extreme Value Theory for understanding the level of activity related to the fine structure of such time-continuous stochastic processes.

Bio: Ana Ferreira is Professor at the Mathematics Department of Lisbon Technology University (IST-UL), Portugal. She completed her PhD in Mathematics with specialization in Extreme Value Theory (EVT) in the Netherlands, through a joint collaboration among EURANDOM (Eindhoven University of Technology), Erasmus University Rotterdam, and Tilburg University. Her core research focuses on both theoretical and applied Extreme Value Theory. She has published in the Annals of Statistics, Annals of Applied Probability and Bernoulli, among others, and co-authored with Laurens de Haan the foundational textbook "Extreme Value Theory: An Introduction", published by Springer in 2006.