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Optimal control of two scale stochastic systems in infinite dimensions: the BSDE approach
Full text linkIn 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
Nonlinear Kolmogorov Equations in Infinite Dimensional Spaces: the Backward Stochastic Differential Equations Approach and Applications to Optimal Control
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The Bismut-Elworthy Formula for Backward SDE's and Applications to Nonlinear Kolmogorov Equations and Control
No full textNull Controllability of an Infinite Dimensional SDE with State and Control-dependent Noise
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Singular Limit of Two-Scale Stochastic Optimal Control Problems in Infinite Dimensions by Vanishing Noise Regularization
Full text linkIn this paper we study the limit of the value function for a two-scale, infinitedimensional, 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 Hamilton-Jacobi-Bellman equations as in [Swiech, ESAIM Control Optim. Calc. Var., to appear] while degeneracy of diffusion coefficients prevents representation as a classical backward stochastic differential equation as in [Guatteri and Tessitore, Appl. Math. Optim., 83 (2021), pp. 1025-1051]. We use a vanishing noise""regularization technique
Asymptotic Behaviour of Infinite Dimensional SDEs by Anticipative Variation of Constants Formula
No full textSpace Regularity of Evolution Equations Driven by Rough Paths
No full textIn this paper, we consider the linear evolution equation dy(t)=Ay(t)dt+∑i=1dGiy(t)dxi(t), where A is a closed operator, associated to a semigroup, with good smoothing effects in a Banach space E, x is a nonsmooth Rd-path, which is η-Hölder continuous for some η∈13,12, and Gi (i=1,...,d) is a non-smoothing linear operator on E. We prove that the Cauchy problem associated with the previous equation admits a unique mild solution and we also show that the solution increases the regularity of the initial datum as soon as time evolves. Then, we show that the mild solution is also an integral solution and this allows us to prove an Itô formula
Composizioni farmaceutiche a rilascio controllato a base di uno o più sali farmaceuticamente accettabili dell'acido gamma idrossibutirrico
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