Singular Limit of BSDEs and Optimal Control of Two Scale Stochastic Systems in Infinite Dimensional Spaces

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...

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Bibliographic Details
Published in:Applied mathematics & optimization Vol. 83; no. 2; pp. 1025 - 1051
Main Authors: Guatteri, Giuseppina, Tessitore, Gianmario
Format: Journal Article
Language:English
Published: New York Springer US 01.04.2021
Springer Nature B.V
Subjects:
Calculus of Variations and Optimal Control; Optimization
Control
Convergence
Differential equations
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Optimal control
Probability
Simulation
Stochastic processes
Stochastic systems
Systems Theory
Theoretical
Stochastic equations in infinite dimensions
Ergodic control
BSDEs
ISSN:0095-4616, 1432-0606
Online Access:Get full text
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Summary: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 is 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.
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ISSN:0095-4616
1432-0606
DOI:10.1007/s00245-019-09577-y