paper

BSDEs with stochastic Lipschitz condition and quadratic PDEs in Hilbert spaces

arXiv:math/0701849 · doi:10.1016/j.spa.2007.06.006

Abstract

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.

BSDEs with stochastic Lipschitz condition and quadratic PDEs in Hilbert spaces · wovepaper