4 papers · 1 filter
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…