Ergodic BSDEs and Optimal Ergodic Control in Banach Spaces

Marco Fuhrman (1) , Ying Hu (2) , Gianmario Tessitore (3)

1 DIPARTIMENTO DI MATEMATICA - Dipartimento di Matematica
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 Dipartimento di Matematica e Applicazioni [Milano]

In this paper we introduce a new kind of Backward Stochastic Differential Equations, called ergodic BSDEs, which arise naturally in the study of optimal ergodic control. We study the existence, uniqueness and regularity of solution to ergodic BSDEs. Then we apply these results to the optimal ergodic control of a Banach valued stochastic state equation. We also establish the link between the ergodic BSDEs and the associated Hamilton-Jacobi-Bellman equation. Applications are given to ergodic control of stochastic partial differential equations.

Mots clés: stochastic optimal control; backward stochastic differential equations; ergodic control; Hamilton-Jacobi-Bellman equation; controlled; stochastic partial differential equations; stochastic differential-equations; parabolic equations; infinite-horizon; hilbert-spaces; elliptic pdes

Domaines: Probabilités [math.PR]

Marco Fuhrman, Ying Hu, Gianmario Tessitore. Ergodic BSDEs and Optimal Ergodic Control in Banach Spaces. SIAM Journal on Control and Optimization, 2009, 48 (3), pp.1542-1566. ⟨10.1137/07069849x⟩. ⟨hal-00165835⟩