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

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.
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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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