1 citations · 2 across the 11 of their papers we have counts for
9 papers · 1 filter
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…
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…
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…