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.

Guatteri, G., Tessitore, G. (2021). Singular Limit of BSDEs and Optimal Control of Two Scale Stochastic Systems in Infinite Dimensional Spaces. APPLIED MATHEMATICS AND OPTIMIZATION, 83(2), 1025-1051 [10.1007/s00245-019-09577-y].

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

Tessitore, G
2021

Abstract

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.
Articolo in rivista - Articolo scientifico
BSDEs; Ergodic control; Stochastic equations in infinite dimensions;
English
1025
1051
27
Guatteri, G., Tessitore, G. (2021). Singular Limit of BSDEs and Optimal Control of Two Scale Stochastic Systems in Infinite Dimensional Spaces. APPLIED MATHEMATICS AND OPTIMIZATION, 83(2), 1025-1051 [10.1007/s00245-019-09577-y].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/230606
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