A probabilistic approach to large time behaviour of mild solutions of Hamilton-Jacobi-Bellman equations in infinite dimension

Ying Hu, Pierre-Yves Madec, Adrien Richou

Published 2014-06-23, updated 2015-01-15Version 2

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.