The Institute for Statistics and Mathematics is pleased to invite you to the next research seminar, taking place on campus:

Gonçalo dos Reis (School of Mathematics, University of Edinburgh)
Simulation of Mean-Field SDEs: Some Recent Results
Wednesday, April 9, 2025, 17:15, in Building D4, Room D4.0.127.

Abstract:
We review recent results on the simulation of McKean-Vlasov stochastic differential equations (MV-SDEs). The first set of results concerns the simulation of MV-SDEs with super-linear growth in both the spatial and interaction components of the drift, along with a non-constant Lipschitz diffusion coefficient.
The second set of results is far more curious. It examines the weak convergence properties of the Laimkuhler-Matthews methods, a non-Markovian Euler-type scheme with the same computational cost as the standard Euler method, for approximating the stationary distribution of a one-dimensional MV-SDE, specifically a mean-field (overdamped) Langevin equation (MFL). Under a strong convexity assumption, we provide both weak and strong error estimates in finite and infinite time horizons. Through a careful analysis of the variation processes and the Kolmogorov backward equation for the associated particle system, we show that the method attains a weak order of convergence rate of 3/2 in the long-time limit - exceeding the standard Euler method’s weak order of 1.
While we use an interacting particle system (IPS) to approximate the MV-SDE, we show the convergence rate is independent of the dimension of the IPS, and this includes establishing uniform-in-time decay estimates for moments of the IPS, the Kolmogorov backward equation and their derivatives. The theoretical findings are supported by numerical experiments.

We aim to stream all on-campus talks via Zoom. A direct link to the stream will be posted on our website.

For further information and the seminar schedule, please see:
www.wu.ac.at/en/statmath/research/resseminar