Singular Perturbation in Multiscale Stochastic Control Problems with Domain Restriction in the Slow Variable
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908483305078784 |
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| author | Calixto, Anderson O. da Costa, Bernardo Freitas Paulo Valle, Glauco |
| author_facet | Calixto, Anderson O. da Costa, Bernardo Freitas Paulo Valle, Glauco |
| contents | We study a multiscale stochastic optimal control problem subject to state constraints on the slow variable. To address this class of problems, we develop a rigorous theoretical framework based on singular perturbation analysis, tailored to settings with constrained dynamics. Our approach relies on the theory of viscosity solutions for degenerate Hamilton-Jacobi-Bellman equations with Neumann-type boundary conditions. We also establish the convergence of the multiscale value functions in the infinite-horizon regime. Finally, we present two illustrative examples that highlight the applicability and effectiveness of the proposed framework. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_14987 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Singular Perturbation in Multiscale Stochastic Control Problems with Domain Restriction in the Slow Variable Calixto, Anderson O. da Costa, Bernardo Freitas Paulo Valle, Glauco Optimization and Control Probability We study a multiscale stochastic optimal control problem subject to state constraints on the slow variable. To address this class of problems, we develop a rigorous theoretical framework based on singular perturbation analysis, tailored to settings with constrained dynamics. Our approach relies on the theory of viscosity solutions for degenerate Hamilton-Jacobi-Bellman equations with Neumann-type boundary conditions. We also establish the convergence of the multiscale value functions in the infinite-horizon regime. Finally, we present two illustrative examples that highlight the applicability and effectiveness of the proposed framework. |
| title | Singular Perturbation in Multiscale Stochastic Control Problems with Domain Restriction in the Slow Variable |
| topic | Optimization and Control Probability |
| url | https://arxiv.org/abs/2505.14987 |