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In this paper we study the limit of the value function for a two-scale, infinite-dimensional, stochastic controlled system with cylindrical noise and possibly degenerate diffusion. The limit is represented as the value function of a new reduced control problem (on a reduced state space). The presence of a cylindrical noise prevents representation of the limit by viscosity solutions of HJB equations, while degeneracy of diffusion coefficients prevents representation as a classical BSDE. We use a vanishing noise regularization technique.
In this paper we study, by probabilistic techniques, the convergence of the value function for a two-scale, infinite-dimensional, stochastic controlled system as the ratio between the two evolution speeds diverges. The value function is represented a
We study a class of infinite-dimensional singular stochastic control problems with applications in economic theory and finance. The control process linearly affects an abstract evolution equation on a suitable partially-ordered infinite-dimensional s
Scenario-based stochastic optimal control problems suffer from the curse of dimensionality as they can easily grow to six and seven figure sizes. First-order methods are suitable as they can deal with such large-scale problems, but may fail to achiev
We derive the explicit solution to a singular stochastic control problem of the monotone follower type with an expected ergodic criterion as well as to its counterpart with a pathwise ergodic criterion. These problems have been motivated by the optim
In this paper we study a class of combined regular and singular stochastic control problems that can be expressed as constrained BSDEs. In the Markovian case, this reduces to a characterization through a PDE with gradient constraint. But the BSDE for