Quadratic BSDEs with random terminal time and elliptic PDEs in infinite dimension
Probability
2013-10-21 v2
Abstract
In this paper we study one dimensional backward stochastic differential equations (BSDEs) with random terminal time not necessarily bounded or finite when the generator F(t,Y,Z) has a quadratic growth in Z. We provide existence and uniqueness of a bounded solution of such BSDEs and, in the case of infinite horizon, regular dependence on parameters. The obtained results are then applied to prove existence and uniqueness of a mild solution to elliptic partial differential equations in Hilbert spaces.
Cite
@article{arxiv.0704.1223,
title = {Quadratic BSDEs with random terminal time and elliptic PDEs in infinite dimension},
author = {Philippe Briand and Fulvia Confortola},
journal= {arXiv preprint arXiv:0704.1223},
year = {2013}
}