ERRATA: 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.

We correct assumption (4.6) in Theorem 4.1 in [F. Gozzi and F. Masiero, SIAM J. Control Optim., 55 (2017), pp. 2981-3012], and we consequently change the proof of Theorem 4.1. We correct the proof of Lemma 5.4 in [F. Gozzi and F. Masiero, SIAM J. Control Optim., 55 (2017), pp. 2981-3012]. 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 the paper [F. Gozzi and F. Masiero, SIAM J. Control Optim., 55 (2017), pp. 3013-3038], too. [ABSTRACT FROM AUTHOR]