An SPDE with Robin-type boundary for a system of elastically killed diffusions on the positive half-line

Ben Hambly, Julian Meier and Andreas Søjmark

Stochastic Processes and their Applications, 2025, vol. 179, issue C

Abstract: We consider a system of particles undergoing correlated diffusion with elastic boundary conditions on the half-line in the limit as the number of particles goes to infinity. We establish existence and uniqueness for the limiting empirical measure valued process for the surviving particles, which is a weak form for an SPDE with a noisy Robin boundary condition satisfied by the particle density. We show that this density process has good L2-regularity properties in the interior of the domain but may exhibit singularities on the boundary at a dense set of times. We make connections to the corresponding absorbing and reflecting SPDEs as the elastic parameter varies.

Keywords: Particle system; Common noise; Mean-field type SPDE; Elastic killing; Robin boundary (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spa.2024.104520

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