Graphon mean field systems

E Bayraktar, S Chakraborty, R Wu - The Annals of Applied …, 2023 - projecteuclid.org
We consider heterogeneously interacting diffusive particle systems and their large
population limit. The interaction is of mean field type with weights characterized by an …

Applications of mean field games in financial engineering and economic theory

R Carmona - arXiv preprint arXiv:2012.05237, 2020 - arxiv.org
This is an expanded version of the lecture given at the AMS Short Course on Mean Field
Games, on January 13, 2020 in Denver CO. The assignment was to discuss applications of …

A case study on stochastic games on large graphs in mean field and sparse regimes

D Lacker, A Soret - Mathematics of Operations Research, 2022 - pubsonline.informs.org
We study a class of linear-quadratic stochastic differential games in which each player
interacts directly only with its nearest neighbors in a given graph. We find a semiexplicit …

Global solutions to the supercooled Stefan problem with blow-ups: regularity and uniqueness

F Delarue, S Nadtochiy, M Shkolnikov - Probability and Mathematical …, 2022 - msp.org
We consider the supercooled Stefan problem, which captures the freezing of a supercooled
liquid, in one space dimension. A probabilistic reformulation of the problem allows us to …

Pathwise McKean–Vlasov theory with additive noise

M Coghi, JD Deuschel, PK Friz, M Maurelli - 2020 - projecteuclid.org
We take a pathwise approach to classical McKean–Vlasov stochastic differential equations
with additive noise, as for example, exposed in Sznitmann (In École D'Été de Probabilités de …

A structure preserving numerical scheme for Fokker-Planck equations of neuron networks: Numerical analysis and exploration

J Hu, JG Liu, Y Xie, Z Zhou - Journal of Computational Physics, 2021 - Elsevier
In this work, we are concerned with the Fokker-Planck equations associated with the
Nonlinear Noisy Leaky Integrate-and-Fire model for neuron networks. Due to the jump …

At the mercy of the common noise: blow-ups in a conditional McKean–Vlasov problem

S Ledger, A Søjmark - 2021 - projecteuclid.org
We extend a model of positive feedback and contagion in large mean-field systems, by
introducing a common source of noise driven by Brownian motion. Although the driving …

[HTML][HTML] Mean field games with absorption and common noise with a model of bank run

M Burzoni, L Campi - Stochastic Processes and their Applications, 2023 - Elsevier
We consider a mean field game describing the limit of a stochastic differential game of N-
players whose state dynamics are subject to idiosyncratic and common noise and that can …

Propagation of minimality in the supercooled Stefan problem

C Cuchiero, S Rigger… - The Annals of Applied …, 2023 - projecteuclid.org
Supercooled Stefan problems describe the evolution of the boundary between the solid and
liquid phases of a substance, where the liquid is assumed to be cooled below its freezing …

Locally interacting diffusions as Markov random fields on path space

D Lacker, K Ramanan, R Wu - Stochastic Processes and their Applications, 2021 - Elsevier
We consider a countable system of interacting (possibly non-Markovian) stochastic
differential equations driven by independent Brownian motions and indexed by the vertices …