Probability Seminar: Thomas Hughes

  • Date: 10/02/2019
  • Time: 15:00
Lecturer(s):

Thomas Hughes, UBC

Location: 

University of British Columbia

Topic: 

Hit and miss with the density of the (\alpha,\beta)-superprocess

Description: 

The (α,β)-superprocess is a spatial branching model associated to an α-stable spatial motion and a (1+β)-stable branching mechanism. Technically, it is a measure-valued Markov process, but this talk concerns the absolutely continuous parameter regime, in which the random measure has a density. After introducing this process and some classical results, I will discuss some newly proven path properties of the density. These include (i) strict positivity of the density at a fixed time (for certain values of α and β) and (ii) a classification of the measures which the density “charges” almost surely, and of the measures which the density fails to charge with positive probability, when conditioned on survival. The duality between the superprocess and a fractional PDE is central to our method, and I will discuss how the probabilistic statements above correspond to new results about solutions to the PDE.

Other Information: 

Location:  ESB 1012