Optimal Control of Unbounded Stochastic Evolution Systems in Hilbert Spaces
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915784456929280 |
|---|---|
| author | Tang, Shanjian Zhou, Jianjun |
| author_facet | Tang, Shanjian Zhou, Jianjun |
| contents | Optimal control and the associated second-order Hamilton-Jacobi-Bellman (HJB) equation are studied for unbounded stochastic evolution systems in Hilbert spaces. A new notion of viscosity solution, featured by absence of B-continuity, is introduced for the second-order HJB equation in the sense of Crandall and Lions, and is shown to coincide with the classical solutions and to satisfy a stability property. The value functional is proved to be the unique continuous viscosity solution to the second-order HJB equation, with the coefficients being not necessarily B-continuous. Our result provides a new theory of viscosity solutions to the HJB equation for optimal control of stochastic evolutionary equations-driven by a linear unbounded operator-in a Hilbert space, and removes the B-continuity assumption on the coefficients which is used in the existing literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_07793 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimal Control of Unbounded Stochastic Evolution Systems in Hilbert Spaces Tang, Shanjian Zhou, Jianjun Optimization and Control Optimal control and the associated second-order Hamilton-Jacobi-Bellman (HJB) equation are studied for unbounded stochastic evolution systems in Hilbert spaces. A new notion of viscosity solution, featured by absence of B-continuity, is introduced for the second-order HJB equation in the sense of Crandall and Lions, and is shown to coincide with the classical solutions and to satisfy a stability property. The value functional is proved to be the unique continuous viscosity solution to the second-order HJB equation, with the coefficients being not necessarily B-continuous. Our result provides a new theory of viscosity solutions to the HJB equation for optimal control of stochastic evolutionary equations-driven by a linear unbounded operator-in a Hilbert space, and removes the B-continuity assumption on the coefficients which is used in the existing literature. |
| title | Optimal Control of Unbounded Stochastic Evolution Systems in Hilbert Spaces |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2602.07793 |