Second order backward stochastic differential equations under a monotonicity condition

Dylan Possamaï (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

In a recent paper, Soner, Touzi and Zhang (2012) [19] have introduced a notion of second order backward stochastic differential equations (2BSDEs), which are naturally linked to a class of fully non-linear PDEs. They proved existence and uniqueness for a generator which is uniformly Lipschitz in the variables y and z. The aim of this paper is to extend these results to the case of a generator satisfying a monotonicity condition in y. More precisely, we prove existence and uniqueness for 2BSDEs with a generator which is Lipschitz in z and uniformly continuous with linear growth in y. Moreover, we emphasize throughout the paper the major difficulties and differences due to the 2BSDE framework.

Domaines: Probabilités [math.PR]

Dylan Possamaï. Second order backward stochastic differential equations under a monotonicity condition. Stochastic Processes and their Applications, 2013, 123 (5), pp.1521-1545. ⟨10.1016/j.spa.2013.01.002⟩. ⟨hal-00919144⟩