Mild solutions of HJB equations associated with cylindrical stable Lévy noise in infinite dimensions
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.
Authors
- Enrico Priola (ORCID: https://orcid.org/0000-0001-7191-6831)
- Alessandro Bondi (ORCID: https://orcid.org/0000-0002-1979-3229)
- Fausto Gozzi (ORCID: https://orcid.org/0000-0003-4755-2841)
- Jerzy Zabczyk
Institutions
- University of Pavia (IT)
- Libera Università Internazionale degli Studi Sociali Guido Carli (IT)
- Polish Academy of Sciences (PL)
Publication Details
- Journal
- Rendiconti Lincei Matematica e Applicazioni
- Published
- 2026-05-11
- DOI
- https://doi.org/10.4171/rlm/1093
- Primary Topic
- Stochastic processes and financial applications
- Type
- article
- Field-Weighted Citation Impact
- 0.00