Interacting reflected diffusions and their hydrodynamic limits
We introduce recent work studying systems of diffusion that interact through their reflection term (local time). We discuss how the hydrodynamic limit of such systems, i.e. the large-scale behavior of the empirical process, will converge to a nonlinear PDE whose solution exhibits interaction with the past values at the boundary. If time allows, we will discuss aspects of the proofs and how the uniqueness of such PDEs follows from a stochastic representation.
Date:
17 June 2019, 12:00 (Monday, 8th week, Trinity 2019)
Venue:
Mathematical Institute, Woodstock Road OX2 6GG
Speaker:
Clayton Barnes (Université de Neuchâtel)
Organising department:
Department of Statistics
Part of:
Probability seminar
Booking required?:
Not required
Audience:
Public
Editor:
Christina Goldschmidt
