- Time: 16:00-17:00 (Beijing Time)
- Date: February 17, 2023
- Venue: MA305 (Online Zoom Meeting ID: 429 579 8090 (Passcode: XJTLU22!))
- Theme: Point process convergence of random walks
In this talk, we study point process convergence for sequences of random walks. First, we focus on point process convergence for sequences of i.i.d. random walks, with the objective of deriving asymptotic theory for the extremes of these random walks. We show convergence of the maximum random walk to the Gumbel or the Fréchet distributions. In particular, we show convergence of the maximum random walk to the Gumbel distribution under the existence of a (2 + 𝛿)th moment. Then, we derive the joint convergence of the off-diagonal entries in sample covariance and correlation matrices of a high-dimensional sample whose dimension increases with the sample size.
Jorge Yslas is a Lecturer in Actuarial Mathematics at the Institute for Financial and Actuarial Mathematics at the University of Liverpool. Previously, Jorge was employed as a Postdoctoral Researcher at the University of Bern, Switzerland, and concluded his Ph.D. studies at the University of Copenhagen under the supervision of Thomas Mikosch and Mogens Bladt. His research interests include extreme value theory, actuarial modeling, applied probability, and statistical theory and applications.