Ergodic BSDEs and related PDEs with Neumann boundary conditions under weak dissipative assumptions

Pierre-Yves Madec (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We study a class of ergodic BSDEs related to PDEs with Neumann boundary conditions. The randomness of the drift is given by a forward process under weakly dissipative assumptions with an invertible and bounded diffusion matrix. Furthermore, this forward process is reflected in a convex subset of $\R^d$ not necessary bounded. We study the link of such EBSDEs with PDEs and we apply our results to an ergodic optimal control problem.

Mots clés: Backward stochastic differential equations; weakly dissipative drift; Neumann boundary conditions; ergodic partial differential equations; optimal ergodic control problem.; optimal ergodic control problem

Domaines: Probabilités [math.PR]

Pierre-Yves Madec. Ergodic BSDEs and related PDEs with Neumann boundary conditions under weak dissipative assumptions. 2013. ⟨hal-00868129v1⟩