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

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.

Mots clés: backward stochastic differential equations; Ornstein-Uhlenbeck operator; HJB equations in infinite dimension; large time behavior; mild solutions; ergodic backward stochastic differential equations

Domaines: Probabilités [math.PR]; Recherche d'information [cs.IR]

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, 2015, 53 (1), pp.378-398. ⟨10.1137/140976091⟩. ⟨hal-01006336v4⟩