تقرير
Mean-field control of non exchangeable systems
| العنوان: | Mean-field control of non exchangeable systems |
|---|---|
| المؤلفون: | De Crescenzo, Anna, Fuhrman, Marco, Kharroubi, Idris, Pham, Huyên |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Probability, Mathematics - Optimization and Control, 60H30, 05C80, 60K35, 93E20 |
| الوصف: | We study the optimal control of mean-field systems with heterogeneous and asymmetric interactions. This leads to considering a family of controlled Brownian diffusion processes with dynamics depending on the whole collection of marginal probability laws. We prove the well-posedness of such systems and define the control problem together with its related value function. We next prove a law invariance property for the value function which allows us to work on the set of collections of probability laws. We show that the value function satisfies a dynamic programming principle (DPP) on the flow of collections of probability measures. We also derive a chain rule for a class of regular functions along the flows of collections of marginal laws of diffusion processes. Combining the DPP and the chain rule, we prove that the value function is a viscosity solution of a Bellman dynamic programming equation in a $L^2$-set of Wasserstein space-valued functions. Comment: 48 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.18635 |
| رقم الأكسشن: | edsarx.2407.18635 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |