1 citations · 1 across the 8 of their papers we have counts for
8 papers
The Depth Ceiling: On the Limits of Large Language Models in Discovering Latent Planning
Yi Xu, Philipp Jettkant, Laura Ruis
The viability of chain-of-thought (CoT) monitoring hinges on models being unable to reason effectively in their latent representations. Yet little is known about the limits of such…
The Atlas Model and SDEs with Boundary Interaction
Philipp Jettkant
We study the mean-field limit of the Atlas model and its connection to SDEs with dependence on the distribution of hitting and local times. The Atlas model describes a system of Br…
A Moving Boundary Problem for Brownian Particles with Singular Forward-Backward Interactions
Philipp Jettkant, Andreas Sojmark
We introduce a system of Brownian particles, each absorbed upon hitting an associated moving boundary. The boundaries are determined by the conditional probabilities of the particl…
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…
Control of Conditional Processes and Fleming--Viot Dynamics
Philipp Jettkant
We discuss equivalent formulations of the control of conditional processes introduced by Lions. In this problem, a controlled diffusion process is killed once it hits the boundary…
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…