In 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.

Guatteri, G., Tessitore, G. (2022). Singular Limit Of Two-Scale Stochastic Optimal Control Problems In Infinite Dimensions By Vanishing Noise Regularization. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 60(1), 575-596 [10.1137/21M1408488].

Singular Limit Of Two-Scale Stochastic Optimal Control Problems In Infinite Dimensions By Vanishing Noise Regularization

Tessitore G.
2022

Abstract

In 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.
Articolo in rivista - Articolo scientifico
optimal control; stochastic equations in infinite dimensions; two-scale systems; vanishing noise;
English
575
596
22
Guatteri, G., Tessitore, G. (2022). Singular Limit Of Two-Scale Stochastic Optimal Control Problems In Infinite Dimensions By Vanishing Noise Regularization. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 60(1), 575-596 [10.1137/21M1408488].
Guatteri, G; Tessitore, G
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/395581
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