A Probabilistic Approach to Large Time Behavior of Mild Solutions of Hamilton-Jacobi-Bellman Equations in Infinite Dimension

Ying Hu 1 Pierre-Yves Madec 2 Adrien Richou 3
1 Research and Development [General Motors]
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 IMB - Institut de Mathématiques de Bordeaux
Abstract : We study the large time behaviour of mild solutions of HJB equations in infinite dimension by a purely probabilistic approach. For that purpose, we show that the solution of a BSDE in finite horizon $T$ taken at initial time behaves like a linear term in $T$ shifted with the solution of the associated EBSDE taken at initial time. Moreover we give an explicit speed of convergence, which seems to appear very rarely in literature.
Keywords : backward stochastic differential equations Ornstein-Uhlenbeck operator HJB equations in infinite dimension large time behavior mild solutions ergodic backward stochastic differential equations
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SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2015, 53 (1), pp.378-398. 〈10.1137/140976091〉
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Dernière modification le : samedi 23 septembre 2017 - 01:08:24
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IRMAR | IMB | INSMI | CHL | IRMAR-PS | UNAM | AGROCAMPUS-OUEST | INRIA | UNIV-RENNES2 | UR2-HB

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Ying Hu, Pierre-Yves Madec, Adrien Richou. A Probabilistic Approach to Large Time Behavior of Mild Solutions of Hamilton-Jacobi-Bellman Equations in Infinite Dimension. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2015, 53 (1), pp.378-398. 〈10.1137/140976091〉. 〈hal-01006336v4〉

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