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

Hambly, Ben, Meier, Julian and Søjmark, Andreas (2025) An SPDE with Robin-type boundary for a system of elastically killed diffusions on the positive half-line. Stochastic Processes and Their Applications, 179. ISSN 0304-4149

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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 L 2-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.

Item Type:	Article
Additional Information:	© 2024 Elsevier B.V
Divisions:	Statistics
Subjects:	Q Science > QA Mathematics
Date Deposited:	13 Nov 2024 09:39
Last Modified:	22 Nov 2024 09:42
URI:	http://eprints.lse.ac.uk/id/eprint/126045

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