BSDEs with stochastic Lipschitz condition and quadratic PDEs in Hilbert spaces
Probability
2008-04-10 v1
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.
Keywords
Cite
@article{arxiv.math/0701849,
title = {BSDEs with stochastic Lipschitz condition and quadratic PDEs in Hilbert spaces},
author = {Philippe Briand and Fulvia Confortola},
journal= {arXiv preprint arXiv:math/0701849},
year = {2008}
}