The webinars will take place on Zoom and a link to the virtual room will be sent out to all those who registered at the registration page.
Speaker: Olfa Draouil (University of Tunis El Manar)
Title: White Noise calculus for time changed Brownian motion
Abstract: In this work, we investigate the time change process \(\Lambda = (\Lambda_{t})_{t \geq 0}\) in the framework of infinite dimensional analysis and especially within White Noise calculus.
We prove that the time changed Brownian motion is a martingale with respect to an associated enlarged filtration as well as its natural one. Also depending on \(\Lambda\), it is not in general a process with independent increments. We define the Hida-Malliavin derivative with respect to the time-changed Brownian motion. Finally, we obtain the Clark Ocone formula with respect to the time changed Brownian motion \(B_{\Lambda}\).
This series of webinars addresses all interested people in probability, stochastic analysis, control, risk evaluation, statistics, with a view towards applications, in particular to renewable energy markets and production. This series brings together the major research themes of the projects STORM, SCROLLER, and SPATUS.