Mild solutions of HJB equations associated with cylindrical stable Lévy noise in infinite dimensions
Abstract
We study the optimal control of an infinite-dimensional stochastic system governed by an SDE in a separable Hilbert space driven by cylindrical stable noise. We establish the existence and uniqueness of a mild solution to the associated HJB equation. This result forms the basis for the proof of the Verification Theorem, which is the subject of ongoing research and will provide a sufficient condition for optimality.
Fields of Study & Subjects
Stochastic processes and financial applications
Stability and Controllability of Differential Equations
stochastic dynamics and bifurcation
Publication details
- Journal / source
- Rendiconti Lincei Matematica e Applicazioni
- Publication date
- 11 May 2026
- Language
- EN