| Issue |
ESAIM: COCV
Volume 32, 2026
|
|
|---|---|---|
| Article Number | 62 | |
| Number of page(s) | 36 | |
| DOI | https://doi.org/10.1051/cocv/2026044 | |
| Published online | 16 July 2026 | |
Particle approximation for conditional control with soft killing
1
Department of Operations Research & Financial Engineering, Princeton University,
Princeton,
NJ
08544,
USA
2
Université Paris Cité and Sorbonne Université, CNRS, LJLL,
F-75005
Paris,
France
* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
27
May
2025
Accepted:
2
June
2026
Abstract
The aim of this paper is to develop a particle approximation for the conditional control problem introduced by P.-L. Lions during his lectures at the College de France in November 2016. We focus on a soft killing relaxed version of the problem, which admits a natural counterpart in terms of stochastic optimal control for a large number of interacting particles. Each particle contributes to the overall population cost through a time-evolving weight that depends on the trajectories of all the other particles. Using recently developed techniques for the analysis of the value function associated with the limiting problem, we establish sharp convergence rates as the number of particles tends to infinity.
Mathematics Subject Classification: 93E20 / 49L25
Key words: Optimal control / mean-field limit / Hamilton–Jacobi equations / conditional control
© The authors. Published by EDP Sciences, SMAI 2026
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