PVSeminar #50

(AEST is the local time in Melbourne = UTC+10 h):

Andreas Kyprianou (The University of Warwick, The United Kingdom of Great Britain and Northern Ireland): Attraction to and repulsion from patches on the hypersphere and hyperplane for isotropic d-dimensional α-stable processes with index α in (0, 1] and dimension 2 or more.

Abstract: Consider a d-dimensional α-stable processes with index in α∈(0,1) and d≥2. Suppose that Ω is a region of the unit sphere S^{d−1} = {x ∈ R^d : |x| = 1}. We construct the aforesaid stable Lévy process conditioned to approach Ω continuously, either from inside S^{d−1}, from outside S^{d−1} or in an oscillatory way; all of which have zero probability. Our approach also extends to the setting of hitting bounded domains of (d-1)-dimensional hyperplanes. We appeal to a mixture of methods, appealing to the modern theory of self-similar Markov process as well as the classical potential analytic view.

Joint work with Tsogzolmaa Saizmaa (National University of Mongolia), Sandra Palau (UNAM, Mexico) and Mateusz Kwasniki (Technical University of Wroclaw).

Zoom meeting link:

https://unimelb.zoom.us/j/89186954006?pwd=bGY2VGVxWXZSOVVXOTBKUlJJdnhJZz09

(if the above link doesn't work when you click it -- please copy & paste it into the address bar in your browser).

Password: 690122 (just in case)

A PDF file with the talk slides (if any) might become available for downloading from our seminar Webpage at https://probvic.wordpress.com/pvseminar/ prior to the talk (the above Zoom link has already been posted there).

Looking forward to seeing you at the forthcoming seminar Zoom meeting,