Dynamic programming in stochastic control of systems with delay

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Optimal control of stochastic delay equations and time-advanced backward stochastic differential equations (2011, background): “There are some papers dealing with this subject in the stochastic Brownian case: we refer to [11, 7, 13, 14, 16].”
When Are HJB-Equations in Stochastic Control of Delay Systems Finite Dimensional? (2003, background): “From [11] we know that the value function satisfies the value function satisfies the dynamic programming principle: Here, X sˆ is the map X sˆ :[− δ ,0]→R defined by X sˆ ( τ )= X ( sˆ + τ ).”
Stochastic optimal control of delay equations arising in advertising models (2004, methodology): “Other approaches to optimal control problems for systems described by SDDEs without infinite dimensional reformulation have been proposed in the literature: for instance, see Elsanosi [6] and Larssen [24] for a more direct application of the dynamic programming principle without appealing to infinit”