BSDEs with stochastic Lipschitz condition and quadratic PDEs in Hilbert spaces

Philippe Briand (1, 2) , Fulvia Confortola (3)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 LAMA - Laboratoire de Mathématiques
3 Dipartimento di Matematica "F. Brioschi"

This paper is devoted to the study of the differentiability of solutions to real-valued backward stochastic differential equations (BSDEs for short) with quadratic generators driven by a cylindrical Wiener process. The main novelty of this problem consists in the fact that the gradient equation of a quadratic BSDE has generators which satisfy stochastic Lipschitz conditions involving BMO martingales. We show some applications to the nonlinear Kolmogorov equations.

Mots clés: BMO-martingales; backward stochastic differential equations; Kolmogorov equations

Domaines: Probabilités [math.PR]

Philippe Briand, Fulvia Confortola. BSDEs with stochastic Lipschitz condition and quadratic PDEs in Hilbert spaces. Stochastic Processes and their Applications, 2008, 118 (5), pp.818-838. ⟨10.1016/j.spa.2007.06.006⟩. ⟨hal-00127337⟩