Errata to: “Stochastic optimal control with delay in the control. I: Solving the HJB equation through partial smoothing” and “Stochastic optimal control with delay in the control. II: Verification theorem and optimal feedbacks”. (English) Zbl 1476.93159
Summary: We correct assumption (4.6) in Theorem 4.1 in our paper [ibid. 55, No. 5, 2981–3012 (2017; Zbl 1375.93140)], and we consequently change the proof of Theorem 4.1. We correct the proof of Lemma 5.4 in [loc. cit.]. Moreover, throughout the paper, starting from formulas (3.13) and (3.14), we notice that the current cost of the control problem cannot depend on the state for the results of the paper to work. This change in the current cost must be made in our paper [ibid. 55, No. 5, 3013–3038 (2017; Zbl 1371.93216)], too.
MSC:
| 93E20 | Optimal stochastic control |
| 60H20 | Stochastic integral equations |
| 47D07 | Markov semigroups and applications to diffusion processes |
| 49L20 | Dynamic programming in optimal control and differential games |
| 35R15 | PDEs on infinite-dimensional (e.g., function) spaces (= PDEs in infinitely many variables) |
Keywords:
optimal control of stochastic delay equations; delay in control; lack of structure condition; second order Hamilton-Jacobi-Bellman equations in infinite dimension; smoothing properties of transition semigroupsReferences:
| [1] | G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions, 2nd ed., Encyclopedia Math. Appl. 152, Cambridge University Press, Cambridge, UK, 2014. · Zbl 1317.60077 |
| [2] | G. Da Prato and J. Zabczyk, Second Order Partial Differential Equations in Hilbert Spaces, London Math. Soc. Lecture Note Ser. 293, Cambridge University Press, Cambridge, UK, 2002. · Zbl 1012.35001 |
| [3] | F. Gozzi and F. Masiero, Stochastic optimal control with delay in the control I: Solving the HJB equation through partial smoothing, SIAM J. Control Optim., 55 (2017), pp. 2981-3012, https://doi.org/10.1137/16M1070128. · Zbl 1375.93140 |
| [4] | F. Gozzi and F. Masiero, Stochastic optimal control with delay in the control II: Verification theorem and optimal feedbacks, SIAM J. Control Optim., 55 (2017), pp. 3013-3038, https://doi.org/10.1137/16M1073637. · Zbl 1371.93216 |
| [5] | F. Gozzi and F. Masiero, Stochastic Optimal Control with Delay in the Control I: Solving the HJB Equation through Partial Smoothing, preprint, https://arxiv.org/abs/1607.06502, 2016. · Zbl 1375.93140 |
| [6] | F. Gozzi and F. Masiero, Stochastic Optimal Control with Delay in the Control II: Verification Theorem and Optimal Feedbacks, preprint, https://arxiv.org/abs/arXiv:1607.06508, 2016. · Zbl 1371.93216 |
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