2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/126372Time-inhomogeneous controlled diffusion processes in both cylindrical and noncylindrical domains are considered. Bellman's principle and its applications to proving the continuity of value functions are investigated.Published at http://dx.doi.org/10.1214/009117906000000395 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)ProbabilityOptimization and Control93E20, 90C40 (Primary)text