COSAM » Events » 2016 » February » Stochastics Seminar

Stochastics Seminar
Time: Feb 25, 2016 (02:00 PM)
Location: Parker Hall 322

Speaker: Olav Kallenberg

Title: Palm trees via extended Brownian snake

Abstract: A Dawson-Watanabe superprocess arises in the diffusion limit from a randomly branching and evolving population in a Euclidean space. Though the limiting process $\xi$ can be thought of as a randomly evolving diffuse cloud, its genealogy is given by a discrete Yule "stick-breaking" process. A fundamental role in the theory is played by the associated Palm trees, which describe the conditional structure of \(\xi\), given that \(\xi_t\) hits some specified points \(x_1,\dots,x_n\). Though the distributions of the latter are suggested by some circumstantial evidence, a formal proof has long been elusive. In this talk, I shall indicate how my Palm tree conjecture, and much more, can be proved by an argument involving an extension of Le Gall's Brownian snake. As always, I will maintain a bird's-eye point of view, trying to avoid the subtle technicalities of the subject.

Last updated: 02/22/2016