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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 as the solution of a backward stochastic differential equation (BSDE) that it is shown to converge towards a reduced BSDE. The noise is assumed to be additive both in the slow and the fast equations for the state. Some non degeneracy condition on the slow equation are required. The limit BSDE involves the solution of an ergodic BSDE and is itself interpreted as the value function of an auxiliary stochastic control problem on a reduced state space.
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 contr
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
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
We study the optimal control of path-dependent McKean-Vlasov equations valued in Hilbert spaces motivated by non Markovian mean-field models driven by stochastic PDEs. We first establish the well-posedness of the state equation, and then we prove the
This paper studies a class of non$-$Markovian singular stochastic control problems, for which we provide a novel probabilistic representation. The solution of such control problem is proved to identify with the solution of a $Z-$constrained BSDE, wit