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.
Bondi, Alessandro; Gozzi, Fausto; Priola, Enrico; Zabczyk, Jerzy. (2026). Mild solutions of HJB equations associated with cylindrical stable Lévy noise in infinite dimensions. ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI, (ISSN: 1120-6330), 1-13. Doi: 10.4171/RLM/1093.
Mild solutions of HJB equations associated with cylindrical stable Lévy noise in infinite dimensions
Alessandro Bondi;Fausto Gozzi;
2026
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.
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