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math.PR2025
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…
math.PR2025
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…
math.PR2025
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…