1 citations · 2 across the 11 of their papers we have counts for
12 papers
Variance-Feedback Noise in Interacting Diffusions: Shape Dynamics and Mean-Field Limits
Ben Hambly, Vinh Nguyen
We study a system of attractive interacting diffusions where the variance feeds back into the noise. That is the common and idiosyncratic Brownian forcing has amplitude $κ(S_t^…
A transform approach to the supercooled Stefan problem
Thomas Blore, Ben Hambly
We consider a generalisation of the probabilistic reformulation of the supercooled Stefan problem from arXiv:1902.05174 allowing for non-integrable initial data. From an applicatio…
A stochastic Fokker--Planck equation for the mean-field limit of a population of noisy integrate-and-fire neurons
Ben Hambly, Aldaïr Petronilia, Christoph Reisinger +1
We study a densely connected system of excitatory integrate-and-fire neurons which are subject to common noise. The system incorporates a gradual transmission of action potentials…
Probabilistic estimates for a system of noisy integrate-and-fire neurons
Ben Hambly, Aldaïr Petronilia, Christoph Reisinger +1
In this note, we establish various probabilistic estimates for an interacting particle system that describes the evolution of the membrane potentials in a network of excitatory int…
Scaling limit for Brownian motions on the -level Sierpinski gaskets: The fractal to Euclidean crossover
David A. Croydon, Ben Hambly, Takashi Kumagai
In two dimensions, the -level Sierpinski gasket is obtained by splitting an equilateral triangle into a collection of equilateral triangles of equal size…
Particle systems and the supercooled Stefan problem with non-integrable initial data
Thomas Blore, D. G. M Flynn, Ben Hambly
We consider an infinite system of particles on the positive real line, initiated from a Poisson point process, which move according to Brownian motion up until the hitting time of…
Particle Systems and McKean--Vlasov Dynamics with Singular Interaction through Local Times
Graeme Baker, Ben Hambly, Philipp Jettkant
We study a system of reflected Brownian motions on the positive half-line in which each particle has a drift toward the origin determined by the local times at the origin of all th…
Non-negative Martingale Solutions to the Stochastic Porous Medium Equation with Sticky Behavior
Ben Hambly, Dörte Kreher, Konstantins Starovoitovs
We construct non-negative martingale solutions to the stochastic porous medium equation in one dimension with homogeneous Dirichlet boundary conditions which exhibit a type of stic…
Optimal Control of the Nonlinear Stochastic Fokker--Planck Equation
Ben Hambly, Philipp Jettkant
We consider a control problem for the nonlinear stochastic Fokker--Planck equation. This equation describes the evolution of the distribution of nonlocally interacting particles af…
Semilinear BSPDEs and Applications to McKean-Vlasov Control with Killing
Ben Hambly, Philipp Jettkant
We introduce a novel class of semilinear nonlocal backward stochastic partial differential equations (BSPDE) on half-spaces driven by an infinite-dimensional càdlàg martingale. The…
Control of McKean--Vlasov SDEs with Contagion Through Killing at a State-Dependent Intensity
Ben Hambly, Philipp Jettkant
We consider a novel McKean--Vlasov control problem with contagion through killing of particles and common noise. Each particle is killed at an exponential rate according to an inte…
Policy Gradient Methods Find the Nash Equilibrium in N-player General-sum Linear-quadratic Games
Ben Hambly, Renyuan Xu, Huining Yang
We consider a general-sum N-player linear-quadratic game with stochastic dynamics over a finite horizon and prove the global convergence of the natural policy gradient method to th…