Posted February 21, 2024
Last modified April 8, 2024
Probability Seminar Questions or comments?
3:30 pm
Jessica Lin, McGill University
Generalized Front Propagation for Stochastic Spatial Models
In this talk, I will present a general framework which can be used to analyze the scaling limits of various stochastic spatial "population" models. Such models include ternary Branching Brownian motion subject to majority voting and several examples of interacting particle systems motivated by biology. The approach is based on moment duality and a PDE methodology introduced by Barles and Souganidis, which can be used to study the asymptotic behaviour of rescaled reaction-diffusion equations. In the limit, the models exhibit phase separation with an evolving interface which is governed by a global-in-time, generalized notion of mean-curvature flow. This talk is based on joint work with Thomas Hughes (Bath).
Posted April 21, 2024
Probability Seminar Questions or comments?
3:30 pm – 4:30 pm Lockett 232
Ben Seeger, The University of Texas at Austin
Equations on Wasserstein space and applications
The purpose of this talk is to give an overview of recent work involving differential equations posed on spaces of probability measures and their use in analyzing mean field limits of controlled multi-agent systems, which arise in applications coming from macroeconomics, social behavior, and telecommunications. Justifying this continuum description is often nontrivial and is sensitive to the type of stochastic noise influencing the population. We will describe settings for which the convergence to mean field stochastic control problems can be resolved through the analysis of the well-posedness for a certain Hamilton-Jacobi-Bellman equation posed on Wasserstein spaces, and how this well-posedness allows for new convergence results for more general problems, for example, zero-sum stochastic differential games of mean-field type.
Posted May 3, 2024
Last modified May 8, 2024
Probability Seminar Questions or comments?
11:00 am – 12:00 pm Zoom
Olga Iziumtseva, University of Nottingham
Asymptotic and geometric properties of Volterra Gaussian processes
In this talk we discuss asymptotic and geometric properties of Gaussian processes defined as $U(t) = \int_0^t K(t, s)dW(s),\ t \geq 0$, where $W$ is a Wiener process and $K$ is a continuous kernel. Such processes are called Volterra Gaussian processes. It forms an important class of stochastic processes with a wide range of applications in turbulence, cancer tumours, energy markets and epidemic models. Le Gall’s asymptotic expansion for the volume of Wiener Sausage shows that local times and self-intersection local times can be considered as the geometric characteristics of stochastic processes that look like a Wiener process. In this talk we discuss the law of the iterated logarithm, existence of local times and construct Rosen renormalized self-intersection local times for Volterra Gaussian processes.