A BPHZ theorem for stochastic PDEs
A classical result obtained in the 50’s and 60’s by Bogoliubov, Parasiuk, Hepp and Zimmerman provides a prescription on how to renormalise amplitudes of Feynman diagrams arising in perturbative quantum field theory in a consistent way. We will discuss an analogue of this theorem which has both an analytic and a probabilistic interpretation. In particular, we will see that it implies that the solutions to a large class of nonlinear stochastic PDEs depend on their driving noise in a surprisingly rigid way. This rigidity is a mathematical manifestation of the “universality” taken for granted when building our intuition on the large-scale behaviour of probabilistic models.
Date:
10 March 2017, 15:30
Venue:
Large Lecture Theatre, LG.03
Speaker:
Professor Martin Hairer (University of Warwick)
Organising department:
Department of Statistics
Organiser:
Professor Arnaud Doucet (University of Oxford)
Organiser contact email address:
events@stats.ox.ac.uk
Part of:
Distinguished Speaker Seminar
Booking required?:
Not required
Audience:
Members of the University only
Editor:
Beverley Lane
