We introduce a new kind of BSDEs called ergodic BSDEs, which arise naturally in the study of optimal ergodic control. We study the existence, uniqueness and regularity of solution to these ergodic BSDEs. Then we apply these results to the optimal ergodic control. We also establish the link between the ergodic BSDE and the ergodic PDE.
Fuhrman, M., Ying, H., Tessitore, G. (2009). Ergodic BSDES and optimal ergodic control in Banach spaces. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 48(3), 1542-1566.
Ergodic BSDES and optimal ergodic control in Banach spaces
TESSITORE, GIANMARIO
2009
Abstract
We introduce a new kind of BSDEs called ergodic BSDEs, which arise naturally in the study of optimal ergodic control. We study the existence, uniqueness and regularity of solution to these ergodic BSDEs. Then we apply these results to the optimal ergodic control. We also establish the link between the ergodic BSDE and the ergodic PDE.
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