Mean Field Control with Absorption

• 成果类型: Article; Early Access
• 署名作者: Cardaliaguet, Pierre; Jackson, Joe; Souganidis, Panagiotis E.
• 署名单位: Universite PSL; Universite Paris-Dauphine; University of Chicago
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X; 1526-5471
• DOI: 10.1287/moor.2025.1233
• 发表日期: 2026-06-05
• 关键词: mean field control; VISCOSITY SOLUTIONS; absorption; Boundary conditions; FINITE-DIMENSIONAL APPROXIMATIONS; jacobi-bellman equations; McKean-Vlasov equation; singular interaction; particle-systems; convergence rate

摘要

In this paper, we study a mean field control problem in which particles are absorbed when they reach the boundary of a smooth domain. The value of the N-particle problem is described by a hierarchy of Hamilton-Jacobi equations which are coupled through their boundary conditions. The value function of the limiting problem, meanwhile, solves a Hamilton-Jacobi equation set on the space of subprobability measures on the smooth domain-that is, the space of nonnegative measures with total mass of at most one. Our main contributions are (i) to establish a comparison principle for this novel infinite-dimensional Hamilton-Jacobi equation and (ii) to prove that the value of the N-particle problem converges in a suitable sense toward the value of the limiting problem as N tends to infinity.