Short-Time Existence and Uniqueness for Some Infinite-Dimensional Nash Systems
Abstract
Abstract. We prove local (in time) existence and uniqueness for a class of infinite-dimensional Nash systems, namely, systems of infinitely many Hamilton–Jacobi–Bellman equations set in an infinite-dimensional Euclidean space. Such systems have been recently showed to arise in the theory of stochastic differential games with interactions governed by sparse graphs by Cirant and the author [ Dyn. Games Appl., 15 (2025), pp. 558–591], given structural assumptions that inspired the hypotheses exploited in the present work. Contextually, we also prove a general linear result, providing a priori estimates, stable with respect to the dimension, for transport-diffusion equations whose drifts (and their derivatives) enjoy appropriate decay properties.
Fields of Study & Subjects
Stability and Controllability of Differential Equations
Advanced Differential Equations and Dynamical Systems
Quantum chaos and dynamical systems
Publication details
- Journal / source
- SIAM Journal on Mathematical Analysis
- Volume
- 58
- Issue
- 2
- Pages
- 1978–1999
- Publication date
- 16 April 2026
- Language
- EN