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

Domaines: Probabilités [math.PR]

Pierre-Yves Madec. Ergodic BSDEs and related PDEs with Neumann boundary conditions under weak dissipative assumptions. Stochastic Processes and their Applications, 2015, 125 (5), pp.1821-1860. ⟨10.1016/j.spa.2014.11.015⟩. ⟨hal-00868129v3⟩