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arXiv · 2504.05230

Mild solutions of HJB equations associated with cylindrical stable L\'evy noise in infinite dimensions

Alessandro Bondi·Fausto Gozzi·Enrico Priola·Jerzy Zabczyk
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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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Alessandro Bondi, Fausto Gozzi, Enrico Priola, Jerzy Zabczyk. 2025-04-07. Mild solutions of HJB equations associated with cylindrical stable L\'evy noise in infinite dimensions. https://arxiv.org/abs/2504.05230

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